NCERT Solutions Class 5 Maths Chapter 8 Weight and Capacity

F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T

C L A S S 5 · M AT H S

NCERT Solutions

Chapter 8: Weight and Capacity

NCERT Textbook — Math Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

104 – 118 20 70 English

Solutions, notes, sample papers & more at 63 pages

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

CLASS 5 · MATHS · MATH MELA

NCERT Solutions — Chapter 8: Weight and Capacity
Chapter 8 of Math Mela is about weight — how heavy a thing is — and capacity — how much a container can
hold. Anu's almirah, a bucket, an ant, a king who gives away wheat, Rathna's grocery shopping, Khayal
chacha's milk cans and Kiran's petrol pump teach four big ideas: pick the right unit (mg, g, kg, quintal, tonne,
ml, l), change one unit into another by multiplying or dividing by 1,000, compare two amounts only after
they are in the same unit, and add, subtract, multiply and divide weights and capacities the same way you
do with plain numbers.

TEXTBOOK BOOK PAGES

Math Mela (Class 5) 104 – 118

SECTIONS QUESTIONS

20 70

MEDIUM

English

Check! Check! — Page 104
Anu's list of weights at home

CHECK! CHECK!

Q1 Anu has recorded the weights of the items in her house. Check if she has recorded
them correctly by putting a tick against them if they look correct. 1. Iron Almirah –
40 g 2. Bed – 60 kg 3. Rice Bag – 5 kg 4. Sofa – 30 g 5. Bucket – 1 kg 800 g 6. Water
Bottle – 650 g 7. Refrigerator – 50 g

Four of them are correct: the Bed, the Rice Bag, the Bucket and the Water Bottle. Put a
tick against 2, 3, 5 and 6.
Here is how to check each one. Ask yourself: can I lift this thing with one hand?

1. If you can lift it easily with one hand, its weight is in grams (g).
2. If it is heavy — you need both hands, or you cannot lift it at all — its weight is in kilograms
(kg).
3. Remember: 1,000 g = 1 kg. So 40 g is less than a small packet of biscuits.

Page 1 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

ITEM ANU TICK? WHY
WROTE

1. Iron 40 g ✗ 40 g is lighter than a small soap bar. An iron almirah is very
Almirah heavy. It should be about 40 kg.

2. Bed 60 kg ✓ A bed is heavy — about the weight of a grown-up person.
Correct.

3. Rice Bag 5 kg ✓ A small rice bag from the shop really is about 5 kg. Correct.

4. Sofa 30 g ✗ 30 g is about the weight of a matchbox. A sofa should be
about 30 kg.

5. Bucket 1 kg 800 g ✓ An empty plastic bucket really is under 2 kg. Correct.

6. Water 650 g ✓ A filled school water bottle is a little more than half a
Bottle kilogram. Correct.

7. 50 g ✗ 50 g is about the weight of an egg. A refrigerator should be
Refrigerator about 50 kg.

Why it happens: Anu did not write wrong numbers. She wrote wrong units. For the
almirah, the sofa and the refrigerator she wrote g where she should have written kg.
A gram is very small — 1,000 grams together make only 1 kilogram. So choosing the
unit is as important as choosing the number.

Check it yourself: Pick up things at home. A pencil, an eraser, a coin — grams. A
school bag, a gas cylinder, a chair — kilograms. Once you feel the difference in your
hands, you will never mix them up.

Let Us Do — Page 104
Read the six weighing scales (a) to (f)

LET US DO

Q1 (a) Read the scale (a). Write the correct weight in the space given below. The dial is
marked 0 at the top and then 1 kg, 2 kg, 3 kg, 4 kg going round. The answer
space says “………… g”.

The needle shows 600 g.

Page 2 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

First learn how any round scale works, then this one is easy.

1. Find the 0. It is at the top. The needle always starts from 0 and turns to the right (clockwise).
2. Find the biggest number. Here it is 4 kg, and it comes back to the same place as 0. So one
full turn of the needle = 4 kg.
3. Count the small marks in one part. Between 0 and 1 kg there are 10 small spaces. So one
small space = 1 kg ÷ 10 = 100 g.
4. Count from 0 to the needle. The needle has gone past the 500 g mark by one more space
— that is 6 spaces from 0.
5. Multiply. 6 spaces × 100 g = 600 g.

0 / 4 kg

3 kg 1 kg

2 kg

Needle at 6 spaces × 100 g = 600 g
One whole turn is 4 kg. Each of the 40 small spaces is 100 g.

Page 3 of 63

as e
Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

co m
e m.
One full turn = 4 kg
m l as
.co
0 to 1 kg = 10 small spaces
m a g
l a se
g
1 small space = 1,000 g ÷ 10 = 100 g
aNeedle is at space number 6

co m
. ag
Reading = 6 × 100 g = 600 g
e m
g l as
a
Check it yourself: 600 g is a little more than half a kilogram, and the needle is a little
past the halfway mark of the first kilogram. That matches.
co m
em.
m l as
.co a g
m Read the scale (b). Write the correct weight in the space given below. The dial is
l a se
g
Q1 (b)
a marked 0 at the top, 1 kg at the bottom and 2 kg back at the top. The answer

s
space says “…… kg ……. g”.
m a
m .co agl
l a se
The needle shows 1 kg 800 g. ag

m
1. One full turn = 2 kg, because 2 kg is written next to the 0.

. co
m
2. Half a turn (straight down) is 1 kg. That mark is written at the bottom.

o m l a se
g
3. Count the small spaces from 0 to the 1 kg mark: there are 10 of them. So one small space =

m .c g ÷ 10 = 100 g. a
s4.e The needle has gone past 1 kg (the bottom) and past the left side, and is pointing up-left.
1,000
a
agl Counting from 0 it is at space number 18.

se m
com a
5. 18 spaces × 100 g = 1,800 g = 1 kg 800 g.

. a g l
m
ase
agl
1 small space = 100 g

Needle at space 18

co m
18 × 100 g = 1,800 g
m .
m as e
.co
1,800 g = 1,000 g + 800 g = 1 kg 800 g
a g l
se m
g l a
a c
.
Why it happens: Once the needle crosses the bottom mark it has already counted 1

s e m
m a
whole kilogram. Everything after that is counted again from 0 — that is why we say 1
kg and 800 g.
e m . co agl
g l as
a

com
m .
m ase
.co


a g l Page 4 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Did you notice? The bucket in Anu's list on the same page also weighs 1 kg 800 g.
This scale could be weighing that very bucket.

Q1 (c) Read the scale (c). Write the correct weight in the space given below. The dial is
marked 0 at the top and then 1 kg, 2 kg, 3 kg, 4 kg, 5 kg, 6 kg going round. The
answer space says “…… kg ……. g”.

The needle shows 2 kg 500 g.

1. One full turn = 6 kg, so the circle is cut into 6 equal kilogram parts.
2. The 1 kg mark is up-right, 2 kg is down-right, and 3 kg is straight down.
3. The needle is pointing down and a little to the right — it lies exactly halfway between the 2
kg mark and the 3 kg mark.
4. Half of 1 kg is 500 g.
5. So the reading is 2 kg + 500 g = 2 kg 500 g.

Full turn = 6 kg

Needle is halfway between 2 kg and 3 kg

Half of 1 kg = 1,000 g ÷ 2 = 500 g

Reading = 2 kg 500 g (= 2,500 g)

Tip: When a needle sits exactly between two numbered marks, the answer is always
the smaller number plus half of one step. Here the step is 1 kg, so we add 500 g.

Q1 (d) Read the scale (d). Write the correct weight in the space given below. The dial is
marked 0 at the top and then 1 kg, 2 kg, 3 kg, 4 kg going round. The answer
space says “…… kg ……. g”.

The needle shows 2 kg 600 g.

1. This dial is the same as scale (a): one full turn = 4 kg, and one small space = 100 g.
2. The 2 kg mark is straight down and the 3 kg mark is on the left.
3. The needle is pointing down-left, past the 2 kg mark, so the answer starts with 2 kg.
4. Counting the small spaces after the 2 kg mark, the needle is 6 spaces along.

Page 5 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

5. 6 × 100 g = 600 g. Reading = 2 kg 600 g.

Needle is past 2 kg → start with 2 kg

6 more small spaces × 100 g = 600 g

Reading = 2 kg 600 g (= 2,600 g)

Why it happens: The needle has gone a little more than half way from the 2 kg mark
to the 3 kg mark. Half way would be 500 g, and it is one space more than that — so
600 g.

Q1 (e) Read the scale (e). Write the correct weight in the space given below. The dial is
marked 0 at the top and then 250 g, 500 g, 750 g and 1 kg going round. The
answer space says “……………. g”.

The needle shows 150 g.

1. One full turn = 1 kg = 1,000 g. This is a small kitchen scale, so it counts in grams.
2. The four big marks are 250 g (right), 500 g (bottom), 750 g (left) and 1 kg (back at the top).
3. The needle is up-right, so it is somewhere between 0 and 250 g.
4. Between 0 and 250 g the dial is cut into 5 equal spaces, so each space is 250 g ÷ 5 = 50 g.
5. The needle is 3 spaces along. 3 × 50 g = 150 g.

Page 6 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

0 / 1 kg

750 g 250 g

500 g

3 spaces × 50 g = 150 g
On this dial a whole turn is only 1 kg, so every space is small — just 50 g.

Full turn = 1,000 g

0 to 250 g = 5 spaces

1 space = 250 g ÷ 5 = 50 g

Needle at space 3 → 3 × 50 g = 150 g

Tip: Two scales can look the same and still mean different things. Always read the
numbers written on the dial before you read the needle.

Page 7 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Q1 (f) Read the scale (f). Write the correct weight in the space given below. The dial is
marked 0 at the top and then 250 g, 500 g, 750 g and 1 kg going round. The
answer space says “……………. g”.

The needle shows 650 g.

1. This dial is the same as scale (e): one full turn = 1 kg = 1,000 g, and one space = 50 g.
2. The needle points down-left. It has passed the 500 g mark at the bottom, so the answer is
more than 500 g.
3. It has not yet reached the 750 g mark on the left, so the answer is less than 750 g.
4. Counting on from 500 g, the needle is 3 spaces along: 3 × 50 g = 150 g.
5. 500 g + 150 g = 650 g.

More than 500 g, less than 750 g
3 spaces past 500 g × 50 g = 150 g

500 g + 150 g = 650 g

Did you notice? Anu's water bottle on the same page also weighs 650 g. Try
weighing your own school water bottle when it is full.

Different Units but Same Measure — Page 105
Two balances, one in kilograms and one in grams

DIFFERENT UNITS BUT SAME MEASURE

Q1 Bags are weighed on two different weighing balances. One weighing balance
displays weight in kilograms and other displays weight in grams. Match the bags
that have the same weights. Weighing Balance 1: 5 kg, 10 kg, 3 kg, 6 kg, 25 kg, 30
kg. Weighing Balance 2: 3,000 g, 6,000 g, 10,000 g, 30,000 g, 5,000 g, 25,000 g.

Every kilogram weight matches the gram weight that is 1,000 times bigger. The two bags in
the picture show it: one balance says 2 kg and the other says 2000 g — and it is the same bag.

1. Remember the rule: 1 kg = 1,000 g.
2. Take a weight from Balance 1 and multiply it by 1,000.
3. Look for that number in Balance 2 and join them.

Page 8 of 63

as e
Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

co m
m.
WEIGHING BALANCE 1 MULTIPLY BY 1,000 WEIGHING BALANCE 2

m as e
5 kg
.co
5 × 1,000 5,000 g
a g l
se m
g l a 10 × 1,000
a
10 kg 10,000 g

3 kg 3 × 1,000 3,000 g

com
m . ag
se
6 kg 6 × 1,000 6,000 g

l a
25 kg
a25g × 1,000 25,000 g

30 kg 30 × 1,000 30,000 g
co m
em.
m l as
.co
Why it happens: The bag does not change. Only the unit changes. A gram is a small
a g
a s emso it takes many grams to make the same weight — exactly one thousand of
gl them for every kilogram. Small unit, big number. Big unit, small number.
unit,
a
m a s
m .co agl
se
Check it yourself: Look at the last three digits. Every gram number here ends in

g l a
three zeros. Cover those three zeros with your finger and the kilogram number is
left. 25,000 g → 25 kg. a

co m
m .
m as e
.co
You can use the double number line given below. Complete it.
a g l
m
Q2

l a se
a g ×3

se m
com g l a
.
1 kg 3 kg 8 kg ____ kg 20 kg ____ kg 30 kg

m a
ase
×1000

agl
1,000 g ____ g ____ g 15,000 g ____ g 25,000 g ____ g

×___

. c om
The double number line printed on page 105. The top line is in kilograms and the bottom

s e m in × ___ .
m a
line is in grams. Fill in every blank, and the missing number

e m . co agl
g l as
a c
.

s e m
m a
co agl
Here is the finished double number line. Each kilogram mark on top sits exactly above its
gram mark below.
m .
as e
a g l

co m
m .
m as e
.co


a g l Page 9 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Top line: kilograms Bottom line: grams (× 1,000 going down)

1 kg 3 kg 8 kg 15 kg 20 kg 25 kg 30 kg

1,000 g 3,000 g 8,000 g 15,000 g 20,000 g 25,000 g 30,000 g

1 kg → 3 kg is × 3, so 1,000 g → 3,000 g is also × 3

Whatever you do to the top number, do the same to the bottom number.

Top line (kg): 1, 3, 8, 15, 20, 25, 30

Bottom line (g): 1,000; 3,000; 8,000; 15,000; 20,000; 25,000; 30,000

The missing multiplier is × 3

1 kg × 3 = 3 kg, and 1,000 g × 3 = 3,000 g

1. Blank on top above 15,000 g: 15,000 ÷ 1,000 = 15 kg.
2. Blank on top above 25,000 g: 25,000 ÷ 1,000 = 25 kg.
3. Blanks below 3 kg, 8 kg, 20 kg, 30 kg: multiply each by 1,000 → 3,000 g, 8,000 g, 20,000 g,
30,000 g.
4. The ×___ arrow at the bottom: it goes from 1,000 g to 3,000 g, and 1,000 × 3 = 3,000. So the
missing number is 3 — the same as the ×3 arrow on top.

Why it happens: The two lines are locked together. Going down from kg to g you
always multiply by 1,000. Going along the line you multiply by whatever you like —
but you must do it on both lines, otherwise the two amounts would stop being
equal.

Q3 Notice the relationship between kg and g.

1 kilogram = 1,000 grams. That one line is the whole relationship.

1. To go from kg to g, multiply by 1,000. Say it as: add three zeros.
2. To go from g to kg, divide by 1,000. Say it as: take away three zeros.

Page 10 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

7 kg = 7 × 1,000 = 7,000 g

7,000 g = 7,000 ÷ 1,000 = 7 kg

Why it happens: A gram is a very tiny weight — about the weight of one grain of a
big rice. You need a thousand of them before you have one kilogram. So the same
bag has a small number when you count in kg and a big number when you count in
g.

Remember this pair: 1,000 g = 1 kg is the twin of 1,000 mg = 1 g and of 1,000 ml = 1
l. The number 1,000 comes back again and again in this chapter.

Let Us Find — Page 106
Shrenu bakes cakes and her scale measures only in grams

LET US FIND

Q1 Shrenu is baking cakes for her shop. She needs 3 kg 500 g flour. Her kitchen scale
measures only in grams. What should her kitchen scale show for 3 kg 500 g of flour?

Her scale should show 3,500 g.
Shrenu's flour comes in two pieces — 3 whole kilograms and 500 loose grams. Change only the
kilogram piece, then join the two.

1. Change the kg part. 1 kg = 1,000 g, so 3 kg = 3 × 1,000 = 3,000 g.
2. Keep the g part as it is. It is already in grams: 500 g.
3. Add the two pieces. 3,000 g + 500 g = 3,500 g.

3 kg = 3 × 1,000 = 3,000 g

3 kg 500 g = 3,000 g + 500 g = 3,500 g

Why it happens: A scale can only speak one language. Shrenu's scale speaks grams.
So she must say the same weight in grams before the scale can understand her.

Page 11 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Check it yourself: Go backwards. 3,500 g = 3,000 g + 500 g = 3 kg + 500 g = 3 kg 500
g✓

Q2 What would be 2 kg 250 g flour in grams?

2 kg 250 g = 2,250 g.

1. Change the kg part. 2 kg = 2 × 1,000 = 2,000 g.
2. The g part stays. 250 g.
3. Add. 2,000 g + 250 g = 2,250 g.

2 kg = 2,000 g

2 kg 250 g = 2,000 g + 250 g = 2,250 g

Tip: There is a quick way to write it. Write the kilogram number, then write the gram
number in three boxes. 2 | 250 → 2,250 g. If the gram part is short, put zeros in
front: 2 kg 50 g → 2 | 050 → 2,050 g.

Let Us Find — Page 106
Shamim and Rehan argue about 5 kg 50 g of sugar

LET US FIND

Q1 Shamim and Rehan observed someone buying sugar weighing 5 kg 50 g. They
thought of the quantity in grams. How much is it? One says 5,050 g and the other
says “No, it is 5,500 g”. Who do you think is right and why?

The one who said 5,050 g is right. 5 kg 50 g = 5,050 g. The answer 5,500 g is wrong.

1. Change the kg part. 5 kg = 5 × 1,000 = 5,000 g.
2. The g part is 50 g — only fifty grams, about the weight of an egg.
3. Add. 5,000 g + 50 g = 5,050 g.

Page 12 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

5 kg 50 g = 5,000 g + 50 g = 5,050 g

The wrong answer 5,500 g would mean 5,000 g + 500 g = 5 kg 500 g

But the sugar is 5 kg 50 g, not 5 kg 500 g

Why the mistake happened: The gram part must always fill three places. Fifty is
written as 0 5 0, not as 5 0 0. Whoever answered 5,500 g wrote 50 in the wrong place
— one column too far to the left — and made the sugar ten times heavier than it
really is.

Try this to be safe: Draw three boxes for the grams before you write. 5 kg 50 g → 5
| 0 5 0 → 5,050 g. 5 kg 500 g → 5 | 5 0 0 → 5,500 g. The boxes stop the mistake.

Q2 Complete the conversions by filling in the blanks. You can use the double number
line given below on which some numbers have been marked.

___ kg ___ kg
1 kg 3 kg ___ kg 7 kg 8 kg ___ kg ___ kg ___ g ___ g

1,000 g ____ g 4,000 g ____ g ____ g 10,000 g 12,000 g ____ g ____ g

The double number line printed on page 106. Some numbers are already marked; fill in
the rest.

Here is the completed double number line.

kilograms on top, the same weight in grams below
1 kg 3 kg 4 kg 7 kg 8 kg 10 kg 12 kg

1,000 g 3,000 g 4,000 g 7,000 g 8,000 g 10,000 g 12,000 g

down = × 1,000 up = ÷ 1,000

Page 13 of 63

as e
Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

The seven marked pairs. Read straight down or straight up.
co m
e m.
m l as
.co a g
s em
Top line (kg): 1, 3, 4, 7, 8, 10, 12
a
gl line (g): 1,000; 3,000; 4,000; 7,000; 8,000; 10,000; 12,000
aBottom

com
1. Blank above 4,000 g: 4,000 ÷ 1,000 = 4 kg.
m . ag
l a se
2. Blank above 10,000 g: 10,000 ÷ 1,000 = 10 kg.
g = 12 kg.
3. Blank above 12,000 g: 12,000 ÷a1,000
4. Blanks under 3 kg, 7 kg, 8 kg: 3,000 g, 7,000 g, 8,000 g.

co m
m.
The last two pairs on the line are left completely blank — the book wants you to choose them.

as e
com l
They must be bigger than 12 kg, and each one has a kg box, a g box and a gram box below. A
. a g
se m
good choice is:

l a
ag 15 kg 500 g ↔ 15,500 g

m a s
.co agl
18 kg 250 g ↔ 18,250 g

se m
g l a
a
Try this: Use the blank ends to mark your own school bag's weight in both units.
Weigh it, write the kg-and-g form on top and the gram form below.
co m
m .
m as e
.co a g l
a s em Complete the conversions by filling in the blanks. (a) 7 kg 67 g = ______ g (b) 3 kg 300
gl
Q3
a g = ______ g (c) 8 kg 69 g = ______ g

se m
com g l a
m . a
ase
agl
(a) 7,067 g (b) 3,300 g (c) 8,069 g
All three go the same way: kilograms into grams. Use the three-box trick — the gram part
always fills three places.

c o m
.
a s em
com
PART KILOGRAM PART GRAM PART IN 3 BOXES ANSWER

e m .(a) 7 kg 67 g agl
as
7 × 1,000 = 7,000 g 067 7,067 g

agl c
.
(b) 3 kg 300 g 3 × 1,000 = 3,000 g 300 3,300 g

s e m
m a
.co agl
(c) 8 kg 69 g 8 × 1,000 = 8,000 g 069 8,069 g

se m
g l a
a

co m
m .
m ase
.co


a g l Page 14 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

(a) 7,000 g + 67 g = 7,067 g

(b) 3,000 g + 300 g = 3,300 g

(c) 8,000 g + 69 g = 8,069 g

Why the zero matters: In (a) the grams are 67, not 670. If you wrote 7,670 g you
would have made the parcel more than half a kilogram heavier. The 0 in front of 67
holds the empty hundreds place, just as it does in money — ₹7 and 67 paise is ₹7.67,
not ₹7.670.

Q4 Complete the conversions by filling in the blanks. (d) 10,760 g = _____ kg ____ g (e)
4,080 g = _____ kg ____ g (f) 12,042 g = _____ kg ____ g

(d) 10 kg 760 g (e) 4 kg 80 g (f) 12 kg 42 g
This time we go the other way — grams into kilograms and grams. There is an easy way to see
it.

1. Count three digits from the right and put your finger there.
2. Everything to the right of your finger is the grams.
3. Everything to the left of your finger is the kilograms.

PART SPLIT IT ANSWER

(d) 10,760 g 10 | 760 → 10,000 g + 760 g 10 kg 760 g

(e) 4,080 g 4 | 080 → 4,000 g + 80 g 4 kg 80 g

(f) 12,042 g 12 | 042 → 12,000 g + 42 g 12 kg 42 g

Why it happens: Every 1,000 grams makes one full kilogram. So the question is
really how many full thousands are hiding inside this number, and what is left over? In
4,080 there are 4 full thousands and 80 left over — that is 4 kg and 80 g.

Check it yourself: Turn each answer back. 4 kg 80 g = 4,000 + 80 = 4,080 g ✓ 12 kg
42 g = 12,000 + 42 = 12,042 g ✓

Page 15 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Comparison between Different Weights — Page 107
Harpreet's picnic basket, and comparing with <, =, >

COMPARISON BETWEEN DIFFERENT WEIGHTS

Q1 Harpreet's family planned a picnic over the weekend. Her mother and father
packed different food items to take along. The following is the list of fruits they
carried — Watermelon – 3 kg, Pineapple – 1 kg 750 g, Apples – 1 kg 250 g, Mangoes –
2 kg. Among the fruits they carried, which one has the (a) highest weight? (b) least
weight? (c) Arrange the items in descending order of their weight.

(a) The watermelon, 3 kg. (b) The apples, 1 kg 250 g. (c) Watermelon, Mangoes, Pineapple,
Apples.
Before comparing, put every weight into the same unit. Grams is the easiest.

1. Change each one to grams. Watermelon 3 kg = 3,000 g. Pineapple 1 kg 750 g = 1,750 g.
Apples 1 kg 250 g = 1,250 g. Mangoes 2 kg = 2,000 g.
2. Now they are all in grams, so just compare the numbers.
3. Order them from biggest to smallest — that is what descending means.

FRUIT WEIGHT IN GRAMS

Watermelon 3 kg 3,000 g

Mangoes 2 kg 2,000 g

Pineapple 1 kg 750 g 1,750 g

Apples 1 kg 250 g 1,250 g

3,000 g > 2,000 g > 1,750 g > 1,250 g

(a) Highest weight → Watermelon (3 kg)

(b) Least weight → Apples (1 kg 250 g)

(c) Descending order → Watermelon (3 kg), Mangoes (2 kg), Pineapple (1 kg 750 g),

Apples (1 kg 250 g)

Page 16 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Why change to grams first: The pineapple and the apples both start with “1 kg”, so
you cannot tell them apart by the kilogram alone. Once both are grams — 1,750 and
1,250 — the answer jumps out.

Total for fun: 3,000 + 2,000 + 1,750 + 1,250 = 8,000 g = 8 kg of fruit. That is a heavy
picnic bag!

Q2 Compare the weights using <, =, > signs. (a) 1 kg 600 g ____ 1,700 g (b) 1 kg 600 g ____ 1
kg 60 g (c) 10 kg 35 g ____ 10035 g (d) 1 kg 600 g ____ 2 kg 500 g (e) 5 kg 50 g ____ 4 kg
500 g (f) 900 g + 7,000 g ____ 7 kg + 900 g

(a) < (b) > (c) = (d) < (e) > (f) =
Use the same three steps every time.

1. Change both sides into grams. Then both sides speak the same language.
2. Compare the two numbers.
3. Write the sign — the open mouth always faces the bigger number.

PART LEFT SIDE IN G RIGHT SIDE IN G SIGN

(a) 1 kg 600 g … 1,700 g 1,600 g 1,700 g <

(b) 1 kg 600 g … 1 kg 60 g 1,600 g 1,060 g >

(c) 10 kg 35 g … 10035 g 10,035 g 10,035 g =

(d) 1 kg 600 g … 2 kg 500 g 1,600 g 2,500 g <

(e) 5 kg 50 g … 4 kg 500 g 5,050 g 4,500 g >

(f) 900 g + 7,000 g … 7 kg + 900 g 7,900 g 7,900 g =

Page 17 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

(a) 1,600 < 1,700 → 1 kg 600 g < 1,700 g

(b) 1,600 > 1,060 → 1 kg 600 g > 1 kg 60 g

(c) 10,035 = 10,035 → 10 kg 35 g = 10035 g
(d) 1,600 < 2,500 → 1 kg 600 g < 2 kg 500 g

(e) 5,050 > 4,500 → 5 kg 50 g > 4 kg 500 g

(f) 900 + 7,000 = 7,900 and 7,000 + 900 = 7,900 → equal

Look carefully at (e). The right side has the bigger gram number (500 against 50),
and that tricks many students. But the kilograms are counted first, and 5 kg beats 4
kg. Kilograms are worth a thousand times more than grams, so they decide first —
just as rupees decide before paise.

Remember the sign: Think of a crocodile's mouth. It always opens towards the
bigger meal. 1,600 < 1,700 — the mouth opens to 1,700.

Milligram — Page 108
How heavy is an ant?

MILLIGRAM

Q1 How much weight can an ant carry? How much does an ant weigh?

An ant weighs only 1 milligram to 5 milligrams. It can carry far more than its own weight.

1. An ant is so light that grams are too big a unit for it. We use milligrams (mg), the smallest
weight unit in this chapter.
2. An ant's own weight is between 1 mg and 5 mg.
3. An ant can pick up a load many times heavier than itself and walk away with it — a leaf, a
grain of sugar, a dead insect much bigger than its own body.

1 g = 1,000 mg

So a 5 mg ant is only 5 parts out of 1,000 parts of one gram

You would need about 200 ants to make just 1 gram (200 × 5 mg = 1,000 mg)

Page 18 of 63

as e
Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

co m
m.
Why this is amazing: If a child weighing 30 kg could lift like an ant, that child would

m l a se
walk about carrying a small car. An ant's body is tiny, so its legs are short and thick
o
.c and that makes them very strong for the weight they a g carry.
m
for their size,

l a se
g
aTry this: Next time you see a line of ants near some spilt sugar, watch one carrying a

co m
ag
grain. Compare the grain with the ant's body. That is the load it is carrying.
m .
as e
a g l
What is a milligram?
m
Q2

co
se m.
o m l a
.c is a very tiny unit of weight. 1,000 milligrams make a1 ggram. We write it as mg.

se m
A milligram

g l a
a
1 g = 1,000 mg
m a s
1 kg = 1,000 g = 10,00,000 mg
m .co agl
l a se
ag

com
× 1,000 × 1,000
m .
m as e
.co mg g
akg l
m g
ase
agl
Going the other way (kg → g → mg) you divide by 1,000 each
se m
omtime. c g l a
m . a
s e
a gla
The weight ladder. Each step up is 1,000 times bigger.

co m
m .
o m l a se
ag a chemist uses.
Where you will meet milligrams: on a medicine strip (a tablet may say 500 mg), on

m .ca gold ornament bill at the jeweller's, and in the tiny weights
l a se
ag Anything so light that grams would be a clumsy unit.

.c
s e m
m a
Let Us Find — Page 108 se m . co agl
a
agl

co m
m .
m ase
.co


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Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Grams into milligrams

LET US FIND

Q1 If a sugar sachet weighs 5 g, how much will it be in milligrams?

5 g = 5,000 mg.

1. Recall the rule. 1 g = 1,000 mg.
2. Multiply the number of grams by 1,000. 5 × 1,000 = 5,000.
3. Write the unit. 5,000 mg.

1 g = 1,000 mg

5 g = 5 × 1,000 = 5,000 mg

Why it happens: Changing g to mg is exactly like changing kg to g. You are going
from a bigger unit to a smaller unit, so you need more of them — a thousand times
more. Bigger unit to smaller unit: multiply.

Did you know? The small sugar sachet you get with tea at a stall really is about 5 g.
That is 5,000 tiny milligrams in one little paper packet.

Q2 Complete the double number line below appropriately.

1000 mg _____ mg 12,000 mg 20,000 mg _____ mg 31,000 mg

1g 5g 12 g _____ g 25 g _____ g

The double number line printed on page 108. The top line is in milligrams, the bottom
line in grams.

Here is the completed double number line.

Page 20 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

milligrams on top, the same weight in grams below
1,000 mg 5,000 mg 12,000 mg 20,000 mg 25,000 mg 31,000 mg

1g 5g 12 g 20 g 25 g 31 g

g → mg: × 1,000 mg → g: ÷ 1,000

Six pairs. Each pair is the same weight said in two ways.

Top line (mg): 1,000; 5,000; 12,000; 20,000; 25,000; 31,000

Bottom line (g): 1; 5; 12; 20; 25; 31

1. Blank above 5 g: 5 × 1,000 = 5,000 mg.
2. Blank below 20,000 mg: 20,000 ÷ 1,000 = 20 g.
3. Blank above 25 g: 25 × 1,000 = 25,000 mg.
4. Blank below 31,000 mg: 31,000 ÷ 1,000 = 31 g.

Check it yourself: Cover the last three zeros of any mg number with your thumb.
What is left is the gram number. 25,000 mg → 25 g ✓

Q3 An ornament weighs 4 g 100 mg. What will be the weight in milligrams?

4 g 100 mg = 4,100 mg.

1. Change the gram part. 4 g = 4 × 1,000 = 4,000 mg.
2. Keep the mg part. 100 mg.
3. Add. 4,000 mg + 100 mg = 4,100 mg.

4 g = 4,000 mg

4 g 100 mg = 4,000 + 100 = 4,100 mg

Page 21 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Why it looks familiar: This is the very same job as changing 4 kg 100 g into 4,100 g.
Only the names of the units changed. The method never changes — multiply the
bigger unit by 1,000 and add the smaller unit.

Q4 A goldsmith has made an ornament weighing 10 g 500 mg. What will its weight be
in milligrams?

10 g 500 mg = 10,500 mg.

1. Change the gram part. 10 g = 10 × 1,000 = 10,000 mg.
2. Keep the mg part. 500 mg.
3. Add. 10,000 mg + 500 mg = 10,500 mg.

10 g = 10,000 mg

10 g 500 mg = 10,000 + 500 = 10,500 mg

Check it yourself: Split 10,500 back. The last three digits are 500 → that is the mg
part. What is left is 10 → that is the gram part. 10 g 500 mg ✓

Did you know? Goldsmiths weigh in very small units because gold is costly. A
mistake of even 100 mg — one tenth of a gram — can change the price of the
ornament.

Let Us Find (continued) — Page 109
Comparing with milligrams; quintals and tonnes

LET US FIND DID YOU KNOW?

Q1 Compare the weights using <, =, > signs. (a) 20 g ____ 200 mg (b) 16 g 50 mg ____ 50 g
16 mg (c) 2,010 mg ____ 2 g 100 mg (d) 9,000 mg ____ 90 g (e) 5,000 g ____ 7,500 g (f) 800
mg + 88 mg ____ 880 mg + 8 mg

(a) > (b) < (c) < (d) < (e) < (f) =
Same three steps as before — but now the small unit is the milligram.

Page 22 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

1. Change both sides into milligrams (or both into grams — either works, as long as they
match).
2. Compare the numbers.
3. Write the sign, open mouth towards the bigger side.

PART LEFT SIDE RIGHT SIDE SIGN

(a) 20 g … 200 mg 20,000 mg 200 mg >

(b) 16 g 50 mg … 50 g 16 mg 16,050 mg 50,016 mg <

(c) 2,010 mg … 2 g 100 mg 2,010 mg 2,100 mg <

(d) 9,000 mg … 90 g 9,000 mg (= 9 g) 90,000 mg <

(e) 5,000 g … 7,500 g 5,000 g 7,500 g <

(f) 800 mg + 88 mg … 880 mg + 8 mg 888 mg 888 mg =

(a) 20,000 > 200 → 20 g > 200 mg

(b) 16,050 < 50,016 → 16 g 50 mg < 50 g 16 mg

(c) 2,010 < 2,100 → 2,010 mg < 2 g 100 mg

(d) 9,000 mg = 9 g, and 9 < 90 → 9,000 mg < 90 g

(e) 5,000 < 7,500 → 5,000 g < 7,500 g

(f) 888 = 888 → equal

Watch out in (b) and (d). Both sides carry the same digits in a different order, or the
same digit with a different unit. 9,000 mg looks like a huge number next to 90 g, but
9,000 mg is only 9 g. The unit decides, not the size of the number.

Tip for (f): You did not even need to convert. Both sides are already in mg, so just
add: 800 + 88 = 888 and 880 + 8 = 888.

Page 23 of 63

as e
Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

co m
m.
Observe the pictures given below and fill in the blank.
e
Q2

m l as
m .co a g
l a se × 40

ag

co m
e m . ag
g l as
a

co m
5,000 kg ………… kg

em.
m l as
.co a g
m An elephant and a blue whale, drawn as in the book. The elephant weighs 5,000 kg and
l a se
a g the whale weighs 40 times as much.

m a s
em
.co agl
a s
glthat is two lakh kilograms, or 200 tonnes.

The whale weighs 2,00,000 kga—

m
1. Write what you know. The elephant weighs 5,000 kg. The arrow says × 40.

. co
m
2. Multiply the easy part first. 5 × 40 = 200.

as e
comthe unit. 2,00,000 kg. g l
3. Put back the three zeros of 5,000. 200 followed by three zeros = 2,00,000.
. a
sem
4. Write
a
agl 5,000 kg × 40
se m
com g l a
= 5 × 40 × 1,000
m . a
ase
agl
= 200 × 1,000

= 2,00,000 kg

co m
m .
m as e
.co
Since 1,000 kg = 1 tonne:
a g l
se m 2,00,000 ÷ 1,000 = 200 tonnes
g l a
a c
m .
m a s e
co agl
Why such a big number: A whale lives in water, and water holds up its body. On

m .
e
land no animal could be that heavy — its legs would break. That is why the biggest

g
animal on earth is a sea animal.
l as
a

co m
m .
m ase
.co


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Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Picture it: 200 tonnes is the weight of about 40 full-grown elephants standing
together. Or about 150 small cars.

Q3 Answer the following questions. (a) 5,000 kg = ______ quintals = _____ tonne (b) 9,000
kg = _____ quintals (c) ______ kg = 8 tonnes

(a) 50 quintals = 5 tonnes (b) 90 quintals (c) 8,000 kg
First, the two new units from the Did you know? box on this page:

100 kg = 1 quintal

10 quintals = 1 tonne

So 1,000 kg = 1 tonne

1. To change kg into quintals, divide by 100. (Take away two zeros.)
2. To change kg into tonnes, divide by 1,000. (Take away three zeros.)
3. To change tonnes into kg, multiply by 1,000. (Add three zeros.)

PART WORKING ANSWER

(a) 5,000 kg = ? quintals 5,000 ÷ 100 50 quintals

(a) 5,000 kg = ? tonne 5,000 ÷ 1,000 5 tonnes

(b) 9,000 kg = ? quintals 9,000 ÷ 100 90 quintals

(c) ? kg = 8 tonnes 8 × 1,000 8,000 kg

Why we need these units: When a truck brings wheat to a godown, saying “this
truck carries 90,00,000 g” would be silly. Big loads get big units. That is why farmers
and traders speak in quintals and tonnes.

Check it yourself: 50 quintals = 50 × 100 kg = 5,000 kg ✓ and 5 tonnes = 5 × 1,000 kg
= 5,000 kg ✓ Both give back the number we started with.

King's Weight — Page 109

Page 25 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

The king donates wheat equal to 10 times his weight

KING'S WEIGHT

Q1 In a kingdom, the king donates wheat grains equal to 10 times his weight on his
birthday. If he donates 800 kg of wheat grain this birthday, what is his current
weight? _______ kg.

The king weighs 80 kg.
We are told the wheat is 10 times the king. So the king is the wheat shared into 10 equal parts.

1. Name what we must find. The king's weight.
2. Write the rule as a picture. King's weight × 10 = wheat donated.
3. Turn it around. If multiplying by 10 gives the wheat, then dividing the wheat by 10 gives the
king.
4. Divide. 800 kg ÷ 10 = 80 kg.

× 10
King = ? kg Wheat = 800 kg

÷ 10 comes back

Going right you multiply by 10. Coming back you divide by 10.

King's weight × 10 = 800 kg

King's weight = 800 ÷ 10

King's weight = 80 kg

Check it yourself: 80 kg × 10 = 800 kg ✓ The wheat matches.

Page 26 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Q2 If he had donated 780 kg of wheat grain on his last birthday, what was his weight
last year? _______ kg.

Last year the king weighed 78 kg.

1. The rule is the same — the wheat is always 10 times the king.
2. Divide the wheat by 10. 780 kg ÷ 10 = 78 kg.

Wheat last year = 780 kg
King's weight last year = 780 ÷ 10 = 78 kg

Why dividing by 10 is easy: When you divide a whole number by 10, you simply
take off one zero, or shift every digit one place to the right. 780 → 78. Try it with 640
(→ 64) and 900 (→ 90).

Check it yourself: 78 kg × 10 = 780 kg ✓

Q3 How much weight did he gain in a year until this birthday? _______ kg.

The king gained 2 kg in the year.

1. Write the two weights. Last year 78 kg. This year 80 kg.
2. Gain means how much more, so subtract the smaller from the bigger.
3. Subtract. 80 kg − 78 kg = 2 kg.

This birthday = 80 kg

Last birthday = 78 kg

Weight gained = 80 − 78 = 2 kg

Another route to the same answer: The extra wheat he gave was 800 − 780 = 20
kg. Since the wheat is 10 times the king, the extra weight of the king is 20 ÷ 10 = 2
kg. Two different roads, one answer — that is a good check.

Page 27 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

From Tiny to Big — The Grocery Store — Page 110
Rathna buys rice for the house and for Pongal

FROM TINY TO BIG THE GROCERY STORE

Q1 Rathna went to the local grocery store and bought several items. She bought 2 kg
500 g rice for daily use and 1 kg 750 g additional rice for the upcoming Pongal
festival. How much total rice did she buy?

Rathna bought 4 kg 250 g of rice in all.
We must find the total rice, so we add the two amounts. There are three ways, and all three give
the same answer. Pick the one you like.
Way 1 — add in your head, like quantities together.

1. Add the kilograms: 2 kg + 1 kg = 3 kg.
2. Add the grams: 500 g + 750 g. Break 750 into 500 + 250. So 500 + 500 = 1,000 g = 1 kg, and
250 g is left over.
3. Join them: 3 kg + 1 kg + 250 g = 4 kg 250 g.

Way 2 — write it in two columns, kg and g.

kg g

2 500

+1 750

―――――――

4 250

The grams made 1,250 g. That is 1 kg and 250 g,

so we write 250 in the g column and carry 1 to the kg column.

Way 3 — change everything to grams first.

Page 28 of 63

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Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

co m
e m.
2 kg 500 g = 2,500 g
m l as
.co
1 kg 750 g = 1,750 g
m a g
l a se
g
2,500 + 1,750 = 4,250 g
a4,250 g = 4 kg 250 g

com
m . ag
l a se
Why we carry 1: The gram column can only hold up to 999. As soon as it reaches
ag and that kilogram must move to the kg column
1,000 it has made a whole kilogram,
— exactly like carrying in ordinary addition, where 10 ones become 1 ten.

co m
em.
m l as
.co g
Remember: we can add and subtract only like quantities — kilograms with
m a
l a se
kilograms, grams with grams. Never add 2 kg to 500 g and call it 502 of anything.

a g
m a s
m.co
How much extra rice did she buy for household use than for the Pongal festival?
agl
se
Q2

g l a
ANSWER a
She bought 750 g extra for household use.
co m
m .
e
“How much extra” means how much more, so we subtract: 2 kg 500 g − 1 kg 750 g.
m l as
.co a g
Way 1 — take away in steps, in your head.

a s em
ag l 1. Start with 2 kg 500 g. Take away 500 g → you have 2 kg.
2. Take away 1 kg → you have 1 kg.
3. You still have to take away 250 g (because 500 + 1,000 + 250 = 1,750 g in all). Take it from the
se m
com g l a
1 kg → you have 750 g.
m . a
as e
g l
Way 2 — two columns, with borrowing.
a

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


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Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

kg g

2 500

−1 750
―――――――

0 750

500 is smaller than 750, so borrow 1 kg = 1,000 g.

Now 1,500 − 750 = 750 in the g column,

and 1 − 1 = 0 in the kg column.

Way 3 — change to grams first.

2,500 g − 1,750 g = 750 g

Why borrowing works here: Borrowing 1 kg gives you 1,000 extra grams, not 10. In
ordinary numbers we borrow 10; in weights, one kilogram is worth a thousand
grams, so that is what crosses over.

Check it yourself: Add the answer back. 1 kg 750 g + 750 g = 1 kg 1,500 g = 2 kg 500
g✓

Let Us Do — Page 111
Seven word problems on adding and subtracting weight

LET US DO

Q1 A restaurant owner uses 5 kg 200 g, 8 kg 900 g, and 12 kg 600 g of onions over 3
days. What is the total weight of onions used by the restaurant owner in 3 days?

He used 26 kg 700 g of onions in three days.

1. Name what we need. The total onions for 3 days, so we add all three amounts.
2. Change each to grams. 5 kg 200 g = 5,200 g; 8 kg 900 g = 8,900 g; 12 kg 600 g = 12,600 g.

Page 30 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

3. Add the grams. 5,200 + 8,900 = 14,100. Then 14,100 + 12,600 = 26,700 g.
4. Change back to kg and g. 26,700 g = 26 kg 700 g.

5,200 g + 8,900 g + 12,600 g = 26,700 g
26,700 g = 26 kg 700 g

Second route (columns): kg column 5 + 8 + 12 = 25 kg. g column 200 + 900 + 600 =
1,700 g = 1 kg 700 g. Carry the 1 kg: 25 + 1 = 26 kg, and 700 g stays. 26 kg 700 g ✓
Same answer.

Q2 Aarav is helping his grandfather at the fruit stall. He lifts two baskets of apples
weighing 2 kg 100 g and 3 kg 950 g. What is the total weight of apples he lifted?

Aarav lifted 6 kg 50 g of apples.

1. Change to grams. 2 kg 100 g = 2,100 g. 3 kg 950 g = 3,950 g.
2. Add. 2,100 + 3,950 = 6,050 g.
3. Change back. 6,050 g = 6 kg 50 g.

2,100 g + 3,950 g = 6,050 g

6,050 g = 6 kg 50 g

Careful here: the leftover is 50 g, not 500 g. 6,050 splits as 6 | 050. Writing 6 kg 500
g would make the apples 450 g heavier than they really are.

Column route: 2 + 3 = 5 kg; 100 + 950 = 1,050 g = 1 kg 50 g; carry the kilogram → 6
kg 50 g ✓

Q3 4 kg 500 g of sand is used from a sack weighing 10 kg. How much sand is left in the
sack?

5 kg 500 g of sand is left.

Page 31 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

1. Name what we need. Sand left = sand at the start − sand used.
2. Change to grams. 10 kg = 10,000 g. 4 kg 500 g = 4,500 g.
3. Subtract. 10,000 − 4,500 = 5,500 g.
4. Change back. 5,500 g = 5 kg 500 g.

10,000 g − 4,500 g = 5,500 g

5,500 g = 5 kg 500 g

Check it yourself: 4 kg 500 g + 5 kg 500 g = 9 kg 1,000 g = 10 kg ✓ The used sand
and the leftover sand together make the full sack.

Q4 A rice sack weighs 9 kg 750 g. After some rice is used, it weighs 3 kg 700 g. How
much rice was used?

6 kg 50 g of rice was used.

1. Name what we need. Rice used = weight at the start − weight now.
2. Change to grams. 9 kg 750 g = 9,750 g. 3 kg 700 g = 3,700 g.
3. Subtract. 9,750 − 3,700 = 6,050 g.
4. Change back. 6,050 g = 6 kg 50 g.

9,750 g − 3,700 g = 6,050 g

6,050 g = 6 kg 50 g

No borrowing needed: 750 is already bigger than 700, and 9 is bigger than 3. So
you can also do it in columns straight away — 9 − 3 = 6 kg and 750 − 700 = 50 g.

Q5 A delivery truck delivered 17 kg 900 g of supplies in the morning and 12 kg 700 g in
the afternoon. How much total supplies did it deliver?

The truck delivered 30 kg 600 g in all.

1. Change to grams. 17 kg 900 g = 17,900 g. 12 kg 700 g = 12,700 g.
2. Add. 17,900 + 12,700 = 30,600 g.

Page 32 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

3. Change back. 30,600 g = 30 kg 600 g.

17,900 g + 12,700 g = 30,600 g

30,600 g = 30 kg 600 g

Column route: 17 + 12 = 29 kg; 900 + 700 = 1,600 g = 1 kg 600 g; carry 1 kg → 30 kg
600 g ✓

Q6 A box of books weighs 14 kg 750 g. After removing some books, the weight of the
box is 10 kg 500 g. What is the weight of the books removed?

The books removed weigh 4 kg 250 g.

1. Name what we need. Books removed = weight before − weight after.
2. Change to grams. 14 kg 750 g = 14,750 g. 10 kg 500 g = 10,500 g.
3. Subtract. 14,750 − 10,500 = 4,250 g.
4. Change back. 4,250 g = 4 kg 250 g.

14,750 g − 10,500 g = 4,250 g

4,250 g = 4 kg 250 g

Check it yourself: 10 kg 500 g + 4 kg 250 g = 14 kg 750 g ✓

Q7 In a community kitchen of a Gurdwara, 65 kg of flour was purchased on one day.
Out of this, 42 kg 275 g flour was used for preparing langar. The next day, an
additional 52 kg 500 g of flour was bought. What is the total quantity of flour now
available in the kitchen store?

75 kg 225 g of flour is now in the store.
This one has two steps. Do them in the order the story happens.

1. Step 1 — take away what was used. 65 kg − 42 kg 275 g.
65,000 g − 42,275 g = 22,725 g = 22 kg 725 g left.

Page 33 of 63

as e
Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

2. Step 2 — add what was bought the next day. 22 kg 725 g + 52 kg 500 g.
co m
22,725 g + 52,500 g = 75,225 g = 75 kg 225 g.
e m.
m l as
m .co a g
l a
Step 1 se
g
a65,000 g − 42,275 g = 22,725 g (= 22 kg 725 g)

co m
em . ag
as
Step 2
22,725 g + 52,500 g = 75,225 g a g l
75,225 g = 75 kg 225 g
co m
se m.
o m l a
g arrived. If you
m .c it in this order: The flour was used before the new flour
a
se first and then subtracted you would still get 75 kg 225 g here, but in many
Why do

g l a
added
a problems the order changes the answer — so make it a habit to follow the story.

om a s
e m . c agl
s
Did you know? Langar is the free community meal served at a Gurdwara to
a
day.
a l
everyone, whoever they are.gKitchens like this really do use flour by the quintal every

co m
m .
as e
. com a g l
More
e mOperations on Weight — Page 112
g l as
a
Multiplying and dividing weights

MORE OPERATIONS ON WEIGHT
se m
com g l a
m. a
ase
agl
Q1 A farmer weighs a sack of potatoes and finds it to be 10 kg 500 g. If the farmer has 4
such potato sacks, what is the total weight of all the sacks?

co m
.

em
m sacks means we multiply. There are two ways. glas
All four sacks together weigh 42 kg.

. c o a
s e m
Four equal

a
agl
Way 1 — multiply the kg and the g separately, then join.

.c
1. Multiply the kilograms: 4 × 10 kg = 40 kg.
s e m
m a
c o agl
2. Multiply the grams: 4 × 500 g = 2,000 g.
3. 2,000 g is 2 whole kilograms, m .
4. Add the two parts: 40 kgla
s e so change it: 2,000 g = 2 kg.

ag
+ 2 kg = 42 kg.

Way 2 — change to grams first, then multiply.

co m
m .
m ase
.co


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Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

10 kg 500 g = 10,500 g

4 × 10,500 = 42,000 g

42,000 g = 42 kg

Four equal sacks

10 kg 500 g 10 kg 500 g 10 kg 500 g 10 kg 500 g
sack 1 sack 2 sack 3 sack 4

40 kg + 2,000 g = 40 kg + 2 kg = 42 kg

Four half-kilograms make two whole kilograms — that is where the extra 2 kg comes from.

Why the 500 g matters so much: Four sacks each carry an extra half kilogram. Four
halves make two wholes. If you forgot the grams you would answer 40 kg and be
short by two full kilograms of potatoes.

Q2 A box of nuts weighing 4 kg 800 g is equally distributed into 4 smaller boxes. What
is the weight of each small box in grams?

Each small box holds 1,200 g (that is 1 kg 200 g).
Sharing equally means we divide. Again, two ways.
Way 1 — divide the kg and the g separately.

1. Divide the kilograms: 4 kg ÷ 4 = 1 kg.
2. Divide the grams: 800 g ÷ 4 = 200 g.
3. Join them: 1 kg 200 g.
4. The question asks for grams, so change it: 1 kg 200 g = 1,200 g.

Way 2 — change to grams first.

4 kg 800 g = 4,800 g

4,800 ÷ 4 = 1,200 g (= 1 kg 200 g)

Page 35 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Why Way 1 worked so neatly: both 4 and 800 divide by 4 without any remainder.
When they do not divide neatly — say 5 kg 300 g ÷ 4 — use Way 2 and change
everything to grams first. Way 2 always works.

Check it yourself: 4 boxes × 1,200 g = 4,800 g = 4 kg 800 g ✓ We are back where we
started.

Let Us Do — Pages 112–113
Cost of groceries, and using double number lines for buying

LET US DO

Q1 The cost of some grocery items is given in the following table. Find the total cost of
each item.

ITEM WEIGHT COST OF 1 KG TOTAL COST

Rice 12 kg 500 g ₹ 60

Flour 7 kg 250 g ₹ 40

Sugar 5 kg ₹ 45

Chana dal 3 kg 600 g ₹ 70

Besan 4 kg ₹ 60

Jaggery 1 kg 400 g ₹ 50

The grocery table printed on page 112. The last column is empty — that is what you
have to find.

Rice ₹750, Flour ₹290, Sugar ₹225, Chana dal ₹252, Besan ₹240, Jaggery ₹70.
For each item, work out the cost of the whole kilograms first, then the cost of the extra grams,
and add.

1. Cost of the whole kilograms = number of kg × cost of 1 kg.

Page 36 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

2. Cost of the extra grams: 500 g is half a kilogram, 250 g is one-fourth, 400 g is four-tenths,
600 g is six-tenths. Take that share of the 1 kg price.
3. Add the two parts.

ITEM WEIGHT COST OF 1 WORKING TOTAL
KG COST

Rice 12 kg 500 ₹60 12 × 60 = 720; half of 60 = 30; 720 + 30 ₹750
g

Flour 7 kg 250 g ₹40 7 × 40 = 280; one-fourth of 40 = 10; 280 ₹290
+ 10

Sugar 5 kg ₹45 5 × 45 ₹225

Chana 3 kg 600 g ₹70 3 × 70 = 210; 600 g costs 6 × 7 = 42; 210 ₹252
dal + 42

Besan 4 kg ₹60 4 × 60 ₹240

Jaggery 1 kg 400 g ₹50 1 × 50 = 50; 400 g costs 4 × 5 = 20; 50 + ₹70
20

Where “6 × 7” comes from: 100 g is one tenth of a kilogram. So 100 g of chana dal
costs ₹70 ÷ 10 = ₹7. Then 600 g costs 6 × ₹7 = ₹42. The same idea gives jaggery: 100
g costs ₹5, so 400 g costs ₹20.

Bill total = 750 + 290 + 225 + 252 + 240 + 70 = ₹1,827

Check one of them a second way: Rice — 12 kg 500 g = 12,500 g. 1,000 g costs ₹60,
so 100 g costs ₹6, so 12,500 g costs 125 × ₹6 = ₹750 ✓

Page 37 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Q2 4 people need 500 g rice for a meal. How much rice will be needed for 8 people if
they eat similar quantity of rice? Complete the double number line below.

×2

4 people 8 people

500 g ………g

×….

The double number line printed on page 112. Fill in the missing weight and the missing
multiplier.

8 people will need 1,000 g of rice, that is 1 kg.

1. Look at the people. 4 people become 8 people. 4 × 2 = 8, so the number of people is
doubled.
2. Do the same to the rice. Whatever you do on the top line, do on the bottom line. So the rice
is doubled too.
3. Double the rice. 500 g × 2 = 1,000 g.
4. Say it in the bigger unit. 1,000 g = 1 kg.

×2

4 people 8 people

500 g 1,000 g = 1 kg
×2
The missing multiplier at the bottom is the same as the one on top: × 2.

Page 38 of 63

as e
Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

co m
em.
4 people → 500 g
m l as
.co
People × 2, so rice × 2
m a g
l a se
g
500 g × 2 = 1,000 g = 1 kg
aThe missing arrow is × 2

com
e m . ag
l as
Try this: How much rice for 12 people? 12 is 4 × 3, so the rice is 500 g × 3 = 1,500 g =
g
1 kg 500 g. a

co m
e m.
m l as
.co a g
Q3 5 kg of tomatoes cost ₹73. How much will 10 kg of tomatoes cost? Complete the

a s em double number line below.

ag l
×2
a s
.com agl
m
ase
agl
5 kg 10 kg

m
.co
₹ 73 ₹ ………

se m
com g l a
m . a
ase
×….

agl The double number line printed on page 113. Fill in the missing cost and the missing
multiplier.
se m
com g l a
m . a
ase
ANSWER agl
m
10 kg of tomatoes will cost ₹146.

. co
e m
as
1. Look at the weight. 5 kg becomes 10 kg. 5 × 2 = 10, so the weight is doubled.
m l
.co a g
2. Double the cost too. The missing arrow is × 2.

s e m3. Work it out. ₹73 × 2. Split it: 70 × 2 = 140 and 3 × 2 = 6.
agla 4. Add. 140 + 6 = ₹146.
.c
s e m
m a
. co agl
5 kg → ₹73
e m
Weight × 2, so cost × 2
g l as
₹73 × 2 = ₹140 + ₹6 = ₹146
a

com
m .
m ase
.co


a g l Page 39 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Why doubling is fair: Twice as many tomatoes must cost twice as much money,
because every kilogram costs the same. This is the whole idea of a double number
line — the two lines move together.

Check it yourself: ₹146 ÷ 2 = ₹73 ✓ Halving the money gives back the price of 5 kg.

Q4 Nitesh is a scrap dealer. How much would he have paid for (a) 16 kg of old
newspaper, if he paid ₹8 for every 1 kg of newspaper? (b) 20 kg iron, if he paid ₹200
for every 10 kg of iron? (c) 10 kg plastic, if he paid ₹30 for 5 kg of plastic? Make
double number lines for answering (b) and (c).

(a) ₹128 (b) ₹400 (c) ₹60
(a) Newspaper — the price is given for 1 kg, so just multiply.

1. 1 kg costs ₹8.
2. 16 kg costs 16 × ₹8.
3. 16 × 8 = 128. So he paid ₹128.

(b) Iron — use a double number line.

×2
10 kg iron 20 kg iron

₹200 ₹400
×2
20 kg is double 10 kg, so the money doubles as well.

10 kg → ₹200

20 kg is 10 kg × 2

So the money is ₹200 × 2 = ₹400

Page 40 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

(c) Plastic — use a double number line again.

×2
5 kg plastic 10 kg plastic

₹30 ₹60
×2
10 kg is double 5 kg, so ₹30 becomes ₹60.

(a) 16 × ₹8 = ₹128

(b) ₹200 × 2 = ₹400

(c) ₹30 × 2 = ₹60

Did you know? A scrap dealer (kabadiwala) buys old newspaper, iron and plastic and
sends them to be used again. Notice that iron fetches ₹20 for a kilogram (₹200 for 10
kg) while plastic fetches only ₹6 a kilogram — the price depends on what the scrap
can be turned into.

Measuring Capacity — Page 113
Choosing between millilitres and litres

MEASURING CAPACITY

Q1 You must have seen tea being prepared at your home. How much water and milk do
we need to make 2 cups of tea? Do we need 1 l of water to make 2 cups of tea? Is
500 ml of water enough for 2 cups of tea?

No, we do not need 1 litre. Yes, 500 ml is more than enough.

1. Start with one cup. A tea cup at home holds about 150 ml.
2. Two cups therefore hold about 150 + 150 = 300 ml of tea in all.

Page 41 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

3. That 300 ml is water and milk together. A common mix is about 200 ml water and 100 ml
milk.
4. Compare with 1 litre. 1 l = 1,000 ml, and we need only about 200 ml of water. So 1 litre is far
too much.
5. Compare with 500 ml. 500 ml is more than 200 ml, so yes, it is enough — with plenty left
over.

1 cup ≈ 150 ml

2 cups ≈ 300 ml of tea

Water needed ≈ 200 ml, milk ≈ 100 ml

1 l = 1,000 ml → far too much

500 ml > 200 ml → enough

Sample answer: “For 2 cups of tea we need about 200 ml of water and about 100 ml
of milk. We do not need 1 litre of water — that would make about 6 or 7 cups. 500 ml
of water is more than enough for 2 cups.”

Check it yourself: At home, fill a tea cup with water and then pour that water into
an empty 1 litre bottle. Count how many cupfuls fill the bottle. You will need about
six or seven — which shows one cup is about 150 ml.

Q2 A bucket can hold a maximum of 20 ml of water. Is this statement correct? Which
unit should be used in such a situation?

No, the statement is not correct. The right unit is the litre (l) — a bucket holds about 20
litres, not 20 millilitres.

1. Think how small 20 ml is. It is about four teaspoons of water. A medicine spoon holds 5 ml.
2. Think how big a bucket is. You can wash with it, or water plants with it. It clearly holds far
more than four spoons.
3. Change the unit, not the number. Millilitres are for spoons, injections and small bottles.
Litres are for buckets, cans and drums.
4. So the sentence should read: a bucket can hold a maximum of about 20 litres of water.

Page 42 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

20 ml = about 4 teaspoons

20 l = 20 × 1,000 = 20,000 ml

That is a thousand times more — and that is a bucket

Why mistakes like this happen: The number 20 sounds right, so the sentence
sounds right. But a measurement is a number and a unit together. Change the unit
and you change the meaning completely — just as ₹20 and ₹20,000 are very
different amounts of money.

Match the unit to the container: medicine spoon 5 ml · glass 250 ml · water bottle
1 l · bucket 20 l · water tank on the roof 500 l or more.

Big to Small, Small to Big — Pages 113–114
Litres into millilitres, and the capacity of containers

BIG TO SMALL, SMALL TO BIG

Q1 Ramiz brings a 500 ml water bottle to school. He drinks two bottles at school. How
much water does he drink at school? Ramiz drinks ______ ml + ______ ml = ______ ml.
Ramiz drinks ____ l of water in a day.

Ramiz drinks 500 ml + 500 ml = 1,000 ml, which is 1 litre.

1. Name what we need. The water he drinks at school.
2. He drinks two bottlefuls, and each bottle is 500 ml. So add 500 ml and 500 ml.
3. 500 + 500 = 1,000 ml.
4. Change to the bigger unit. 1,000 ml = 1 l.

Page 43 of 63

as e
Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

co m
e m.
500 ml + 500 ml = 1,000 ml
m l as
1,000 ml = 1 l
m .co a g
l a se
g
aSo the blanks are:

co m
. ag
Ramiz drinks 500 ml + 500 ml = 1,000 ml
e m
Ramiz drinks 1 l of water
g l as
a
m
Two half-litre bottles make one litre m.co
m as e
.co a g l
se m
g l a
a 1,000 ml
500 ml + 500 ml = s
m a
.co agl
=1l
sem
g l a
a

co m
m .
e
Two 500 ml bottles fill exactly one litre — just as two 500 g weights make one kilogram.

m l as
.co
m This 1 litre is only what Ramiz drinks at school. He will drink more at home.a g
a s eNote:
agl Doctors say a child should drink about 2 litres of water in a whole day.

se m
com g l a
m . a
e
as in a day. How many times would she need to refill a 500
Q2
g l
a Muskaan drinks _________ ml of water in a day.
Muskaan drinks 3 l of water
ml water bottle? ________.

co m
m .
e

m l as
.co g
She would fill the bottle 6 times. She drinks 3,000 ml in a day.
a
em1. Make the units match. The water is in litres, the bottle is in millilitres. Change litres to
a s
agl
c
millilitres: 3 l = 3 × 1,000 = 3,000 ml.

m .
2. Name what we need. How many 500 ml bottlefuls fit inside 3,000 ml.
m a s e
. c o agl
3. Divide. 3,000 ÷ 500 = 6.

a s
4. So she fills the bottle 6 times.em
agl

co m
m .
m ase
.co


a g l Page 44 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

3 l = 3 × 1,000 = 3,000 ml

3,000 ml ÷ 500 ml = 6 bottles

An easier way to see it: Two 500 ml bottles make 1 litre. So for 3 litres she needs 2 ×
3 = 6 bottles. Same answer, no long division.

Check it yourself: 6 × 500 ml = 3,000 ml = 3 l ✓

Q3 Write the total capacity of the following containers in each blank. First set: a 1 l jar,
a 500 ml jar and a 100 ml jar. Second set: a 1 l jar and a 500 ml jar. Third set: a 100 ml
jar, a 100 ml jar and a 500 ml jar. Fourth set: a 1 l jar, a 1 l jar and a 100 ml jar. Each
blank reads ____ l ________ ml.

Set 1: 1 l 600 ml Set 2: 1 l 500 ml Set 3: 0 l 700 ml Set 4: 2 l 100 ml
“Total capacity” means: if you filled every jar right up to its top mark, how much liquid would you
have altogether?

1. Read the top mark on each jar. That is what it holds when full.
2. Change every reading to millilitres so they can be added (1 l = 1,000 ml).
3. Add them all.
4. Write the answer as litres and millilitres.

SET JARS IN ML TOTAL ANSWER

1 1 l + 500 ml + 100 ml 1,000 + 500 + 100 1,600 ml 1 l 600 ml

2 1 l + 500 ml 1,000 + 500 1,500 ml 1 l 500 ml

3 100 ml + 100 ml + 500 ml 100 + 100 + 500 700 ml 0 l 700 ml

4 1 l + 1 l + 100 ml 1,000 + 1,000 + 100 2,100 ml 2 l 100 ml

Page 45 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

1l

500 ml

100 ml = 1,600 ml
= 1 l 600 ml

1,000 ml 500 ml 100 ml
Set 1: read the top mark of each jar and
add
The tallest number printed on a jar is its full capacity.

Why Set 3 begins with 0 l: 700 ml has not reached 1,000 ml, so there is not even
one whole litre. We write 0 l 700 ml — the same way we write ₹0 and 70 paise when
there is no whole rupee.

Check Set 4 a second way: two 1 litre jars are already 2 litres, and one more 100 ml
jar is added. So 2 l 100 ml ✓

Different Units but Same Measure — The Milkman's Delivery — Page 114
Khayal chacha delivers milk to five families

DIFFERENT UNITS BUT SAME MEASURE THE MILKMAN'S DELIVERY

Q1 Bhalerao's family orders 2 l of milk everyday. This family has a vessel marked in ml
only. What mark will you see in the vessel corresponding to 2 l?

The milk will come up to the 2,000 ml mark.

1. Recall the rule. 1 l = 1,000 ml.
2. Multiply the litres by 1,000. 2 × 1,000 = 2,000.
3. Write the unit. 2,000 ml.

Page 46 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

1 l = 1,000 ml

2 l = 2 × 1,000 = 2,000 ml

Why it matters: The milk is the same milk. Only the marking on the vessel is
different. A vessel marked in ml cannot show “2 l”, so it shows the same amount
using a bigger number of smaller units.

Tip: This is the twin of 2 kg = 2,000 g from page 105. Litres and kilograms behave in
exactly the same way, because both use the number 1,000.

Q2 Complete the double number line.

1l 2l 6l 8l ____ l 14 l ____ l ____ l

1000 ml 2000 ml ____ ml ____ ml 12,000 ml ____ ml 20,000 ml 25,000 ml

The double number line printed on page 114. The top line is in litres, the bottom line in
millilitres.

Here is the completed double number line.

litres on top · millilitres below (all bottom numbers are in ml)
1l 2l 6l 8l 12 l 14 l 20 l 25 l

1,000 2,000 6,000 8,000 12,000 14,000 20,000 25,000

l → ml: × 1,000 ml → l: ÷ 1,000

Eight pairs. Read straight down to change litres into millilitres.

Page 47 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Top line (l): 1, 2, 6, 8, 12, 14, 20, 25

Bottom line (ml): 1,000; 2,000; 6,000; 8,000; 12,000; 14,000; 20,000; 25,000

1. Below 6 l: 6 × 1,000 = 6,000 ml.
2. Below 8 l: 8 × 1,000 = 8,000 ml.
3. Above 12,000 ml: 12,000 ÷ 1,000 = 12 l.
4. Below 14 l: 14 × 1,000 = 14,000 ml.
5. Above 20,000 ml: 20 l. Above 25,000 ml: 25 l.

Check it yourself: Every ml number on this line ends in three zeros, because every
litre value is a whole number. Cover the three zeros and the litre number appears.

Q3 Khayal chacha delivers the following amounts of milk each week to different
families. Complete the table.

FAMILY MILK DELIVERED IN A WEEK IN L QUANTITY IN ML

Arora’s 8

Nair’s 14

Shrivastava’s 12,000

Das’s 20,000

Rao’s 25,000

The milk delivery table printed on page 114. Fill in every empty cell.

Arora's 8,000 ml · Nair's 14,000 ml · Shrivastava's 12 l · Das's 20 l · Rao's 25 l.

1. If the litres are given, multiply by 1,000 to get millilitres.
2. If the millilitres are given, divide by 1,000 to get litres.

Page 48 of 63

as e
Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

co m
m.
FAMILY MILK DELIVERED IN A WEEK IN L QUANTITY IN ML

m as e
Arora's
.co
8
a g l
8,000 ml

se m
g l a
Nair's 14
a
14,000 ml

Shrivastava's 12 12,000

co m
Das's 20
e m . 20,000 ag
g l as
Rao's 25
a 25,000

co m
8 l = 8 × 1,000 = 8,000 ml
e m.
m l as
.co a g
em ml = 12,000 ÷ 1,000 = 12 l
14 l = 14 × 1,000 = 14,000 ml

a s
gl
12,000
a 20,000 ml = 20 l
m a s
.co agl
25,000 ml = 25 l
se m
g l a
a
Think about it: Rao's family takes 25 l in a week. That is 25 ÷ 7, which is a little more
than 3 l a day — a big family, or one that makes a lot of curd and paneer.
co m
m .
o m l a se
m .c for fun: 8 + 14 + 12 + 20 + 25 = 79 litres of milk eachagweek from these five
Total

asehouses alone.
agl
se m
com g l a
m . a
ase
Let Us Think — Page 115
agl
Mary and Daisy's bottle, and converting litres and millilitres

LET US THINK

co m
m .
o m l a seThey wondered about the
.c capacity of the bottle in ml. How much is it? One saysag 1,400 ml and the other says
Q1 Mary and Daisy filled their bottle with 1 l 400 ml of water.

se m
g l a “No, it is 1,040 ml.” Who do you think is correct and why?
a c
m .
m a s e
co agl

m .
e
The one who said 1,400 ml is correct. 1 l 400 ml = 1,400 ml. The answer 1,040 ml is wrong.

g l as
a
1. Change the litre part. 1 l = 1,000 ml.
2. Keep the ml part. 400 ml.

com
m .
m ase
.co


a g l Page 49 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

3. Add. 1,000 ml + 400 ml = 1,400 ml.

1 l 400 ml = 1,000 + 400 = 1,400 ml

The wrong answer 1,040 ml would mean 1,000 + 40 = 1 l 40 ml

But the bottle holds 400 ml extra, not 40 ml

Why the mistake happened: The ml part must fill three places. Four hundred is
written 4 0 0. Whoever answered 1,040 wrote 40 instead of 400 — they slipped one
column and lost 360 ml, more than a glassful.

Use the boxes again: 1 l | 4 0 0 ml → 1,400 ml. 1 l | 0 4 0 ml → 1,040 ml. Three
boxes, always.

Q2 Convert and fill in the blanks appropriately. You can use the double number line
given earlier. (a) 3 l 8 ml = _____ ml (b) 9 l 90 ml = _____ ml (c) 14,075 ml = ____ l ____ ml (d)
8 l 86 ml = ____ ml (e) 12,200 ml = ____ l _____ ml (f) 18,350 ml = ____ l ____ ml

1l 2l 6l 8l ____ l 14 l ____ l ____ l

1000 ml 2000 ml ____ ml ____ ml 12,000 ml ____ ml 20,000 ml 25,000 ml

The double number line printed on page 114. The top line is in litres, the bottom line in
millilitres.

(a) 3,008 ml (b) 9,090 ml (c) 14 l 75 ml (d) 8,086 ml (e) 12 l 200 ml (f) 18 l 350 ml
Three of these go one way and three go the other way. Sort them first.
Litres and millilitres → millilitres (parts a, b, d): multiply the litres by 1,000 and add the ml,
keeping three boxes for the ml.
Millilitres → litres and millilitres (parts c, e, f): count three digits from the right; those are the
ml, and the rest are the litres.

Page 50 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

PART WORKING ANSWER

(a) 3 l 8 ml 3,000 + 008 3,008 ml

(b) 9 l 90 ml 9,000 + 090 9,090 ml

(c) 14,075 ml 14 | 075 14 l 75 ml

(d) 8 l 86 ml 8,000 + 086 8,086 ml

(e) 12,200 ml 12 | 200 12 l 200 ml

(f) 18,350 ml 18 | 350 18 l 350 ml

Look hard at (a). Only 8 millilitres — less than two teaspoons. In the three boxes it
becomes 0 0 8, so the answer is 3,008 ml. Writing 3,800 ml would be a huge mistake,
almost 800 ml too much.

Check them all: turn each answer back. 3,008 → 3 | 008 → 3 l 8 ml ✓ 14 l 75 ml →
14,000 + 75 = 14,075 ✓

Let Us Compare — Pages 115–117
Kiran's petrol pump, and Sam and Tina's bikes

LET US COMPARE

Q1 Kiran owns a petrol pump. She records the details of the sales of petrol in a day.
Complete the “Total Quantity of Fuel (in litres)” column. Truck — 3 vehicles, 500 l
each. Bus — 6 vehicles, 300 l each. Car — 10 vehicles, 50 l each. Auto Rickshaw — 12
vehicles, 8 l each. Two-wheeler — 25 vehicles, 5 l each.

Truck 1,500 l · Bus 1,800 l · Car 500 l · Auto Rickshaw 96 l · Two-wheeler 125 l.

1. For each row, ask: how many vehicles, and how much fuel in each?
2. Multiply the number of vehicles by the fuel in one vehicle.
3. Write the unit — litres.

Page 51 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

VEHICLE NO. OF QUANTITY OF FUEL IN WORKING TOTAL QUANTITY
VEHICLES EACH VEHICLE (IN OF FUEL (IN
LITRES) LITRES)

Truck 3 500 3 × 500 1,500 l

Bus 6 300 6 × 300 1,800 l

Car 10 50 10 × 50 500 l

Auto 12 8 12 × 8 96 l
Rickshaw

Two- 25 5 25 × 5 125 l
wheeler

Notice something interesting: there are only 3 trucks but 25 two-wheelers, and yet
the trucks take twelve times more fuel. A big vehicle drinks a lot in one go. The
number of vehicles alone does not tell you the fuel.

Q2 How much more fuel is bought for buses than for trucks?

300 litres more fuel is bought for buses.

1. Take the two totals from the table. Buses 1,800 l, trucks 1,500 l.
2. “How much more” means subtract the smaller from the bigger.
3. 1,800 − 1,500 = 300 l.

Buses = 6 × 300 = 1,800 l

Trucks = 3 × 500 = 1,500 l

Difference = 1,800 − 1,500 = 300 l

Check it yourself: 1,500 l + 300 l = 1,800 l ✓ The trucks' fuel plus the difference gives
the buses' fuel.

Page 52 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Q3 What is the total quantity of fuel filled from the petrol pump on that day?

4,021 litres of fuel were filled that day.

1. Take all five totals from the last column: 1,500 l, 1,800 l, 500 l, 96 l, 125 l.
2. Add the big ones first. 1,500 + 1,800 = 3,300. Then 3,300 + 500 = 3,800.
3. Add the small ones. 96 + 125 = 221.
4. Add the two parts. 3,800 + 221 = 4,021 l.

1,500 + 1,800 + 500 + 96 + 125

= 3,800 + 221

= 4,021 litres

Why group the numbers: Adding five numbers at once is easy to get wrong.
Grouping the round hundreds together and the small numbers together makes each
step simple enough to do in your head.

Did you notice? 4,021 litres is more than four tonnes of petrol in a single day — and
that is only one small petrol pump.

Q4 Compare the following quantities using the signs <, =, >. (a) 5 l 600 ml ____ 5,400 ml
(b) 10 l 100 ml ____ 1 l 600 ml (c) 190 ml + 800 ml ____ 800 ml + 109 ml (d) 3 l 600 ml ____
3,600 ml (e) 4 l 50 ml ____ 4 l 500 ml

(a) > (b) > (c) > (d) = (e) <
Same method as with weights: put both sides into millilitres, then compare.

Page 53 of 63

as e
Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

co mSIGN
m.
PART LEFT SIDE IN ML RIGHT SIDE IN ML

m as e
.co
(a) 5 l 600 ml … 5,400 ml 5,600 ml 5,400 ml
a g l >

se m
g l a 10,100 ml 1,600 ml
a
(b) 10 l 100 ml … 1 l 600 ml >

(c) 190 + 800 … 800 + 109 990 ml 909 ml >

co m
(d) 3 l 600 ml … 3,600 ml 3,600 ml
e m . 3,600 ml = ag
g l amls
(e) 4 l 50 ml … 4 l 500 ml
a
4,050 4,500 ml <

co m
(a) 5,600 > 5,400
e m.
m l as
m .co
(b) 10,100 > 1,600
a g
a s e990
gl
(c) > 909
a (d) 3,600 = 3,600
m a s
.co agl
(e) 4,050 < 4,500
se m
g l a
a
Part (c) is a trap worth studying. Both sides use the digits 1, 9 and 0, and both add
800. But 190 is much more than 109 — the 9 is in the tens place on the left and in
co m
m .
e
the ones place on the right. Place value decides.
m l as
.co a
m (b) needs no working at all: 10 litres is already far more than 1 litre, so the
g
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agl answer is > whatever the millilitres are. Always look at the bigger unit first.

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instheir bikes. Tina bought 2 l 500 ml of petrol. Sam bought 2
Sam and Tina fill petrolla
Q5
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l 800 ml more petrolathan Tina. How much petrol did Sam buy?

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Sam bought 5 l 300 ml of petrol.

a s emThe word more tells us to add. Sam took everything Tina took, and 2 l 800 ml on top of that.
agl Way 1 — add like quantities.
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1. Add the litres: 2 l + 2 l = 4 l.

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2. Add the millilitres: 500 ml + 800 ml = 1,300 ml.
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3. 1,300 ml is 1 whole litre and 300 ml left over.
l +g300 ml = 5 l 300 ml.
4. So the total is 4 l + 1 a

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Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Way 2 — change to millilitres first.

2 l 500 ml = 2,500 ml

2 l 800 ml = 2,800 ml
2,500 + 2,800 = 5,300 ml

5,300 ml = 5 l 300 ml

Column form

l ml

2 500

+2 800

――――――

5 300 (carry 1 l because the ml crossed 1,000)

Read the question carefully: Sam bought 2 l 800 ml more than Tina — not 2 l 800 ml
in total. If you had answered 2 l 800 ml you would have missed Tina's amount
completely.

Q6 After refueling, Sam found his fuel gauge reading 9 l. How much fuel did his bike
have before refueling?

Sam's bike had 3 l 700 ml of fuel before refuelling.

1. Name the parts. Fuel before + fuel filled = fuel after.
2. We know two of them. Fuel filled = 5 l 300 ml (from the last question). Fuel after = 9 l.
3. So subtract. Fuel before = 9 l − 5 l 300 ml.
4. Change to millilitres. 9 l = 9,000 ml. 5 l 300 ml = 5,300 ml.
5. Subtract. 9,000 − 5,300 = 3,700 ml = 3 l 700 ml.

Page 55 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

The two parts together make the whole tank reading

before = ? filled = 5 l 300 ml

after = 9 l
When two parts make a whole and you know one part, subtract to find the other.

Column form

l ml

9 000

−5 300

――――――

3 700 (borrow 1 l = 1,000 ml)

Or in ml only: 9,000 − 5,300 = 3,700 ml = 3 l 700 ml

Check it yourself: 3 l 700 ml + 5 l 300 ml = 8 l 1,000 ml = 9 l ✓ That matches the
gauge exactly.

Let Us Solve — Page 118
Picnic bottles, milk glasses, orange juice and oil

LET US SOLVE

Q1 Riya is filling water bottles for a picnic. She fills one 2 l bottle and four 500 ml
bottles. Her friend, Aarav fills three 750 ml bottles. Who filled more water, Riya or
Aarav? How much more?

Riya filled more water — 1 l 750 ml more than Aarav.

Page 56 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

1. Find Riya's water. One 2 l bottle = 2,000 ml. Four 500 ml bottles = 4 × 500 = 2,000 ml.
Riya's total = 2,000 + 2,000 = 4,000 ml = 4 l.
2. Find Aarav's water. Three 750 ml bottles = 3 × 750 = 2,250 ml = 2 l 250 ml.
3. Compare. 4,000 ml is more than 2,250 ml, so Riya filled more.
4. Find how much more. 4,000 − 2,250 = 1,750 ml = 1 l 750 ml.

Riya = 2,000 ml + (4 × 500 ml) = 2,000 + 2,000 = 4,000 ml

Aarav = 3 × 750 ml = 2,250 ml

Difference = 4,000 − 2,250 = 1,750 ml = 1 l 750 ml

Why we changed everything to ml first: Riya's water was given partly in litres and
partly in millilitres. You cannot compare 2 l with 750 ml by looking. One unit for
everything, and the comparison becomes easy.

Check it yourself: 2,250 ml + 1,750 ml = 4,000 ml ✓ Aarav's water plus the
difference gives Riya's water.

Q2 (a) A bottle of milk is poured equally into 8 glasses, leaving 120 ml of milk in the
bottle. If each glass has a capacity of 360 ml, what is the total capacity of 8
glasses?

The 8 glasses hold 2,880 ml altogether, which is 2 l 880 ml.

1. Name what we need. Milk in 8 equal glasses.
2. One glass holds 360 ml, so multiply by 8.
3. Break the multiplication up. 300 × 8 = 2,400 and 60 × 8 = 480.
4. Add. 2,400 + 480 = 2,880 ml.
5. Say it in litres too. 2,880 ml = 2 l 880 ml.

8 × 360 ml

= 8 × 300 + 8 × 60

= 2,400 + 480

= 2,880 ml = 2 l 880 ml

Page 57 of 63

Class 5 Maths Chapter 8 Weight and Capacity AglaSem · NCERT Solutions

Check it yourself: 2,880 ÷ 8 = 360 ✓ Sharing the total back into 8 glasses gives one
glassful.

Q2 (b) How much milk was there in the bottle initially?

The bottle held 3,000 ml of milk at the start — that is exactly 3 litres.

1. Where did the milk go? Some went into the 8 glasses, and 120 ml stayed in the bottle.
2. Milk in the glasses = 2,880 ml (from part a).
3. Milk left in the bottle = 120 ml.
4. Add the two. 2,880 + 120 = 3,000 ml = 3 l.

The two parts add up to the milk that was in the bottle

poured into 8 glasses = 2,880 ml left 120 ml

whole bottle = 3,000 ml = 3 l
Poured out plus left over equals what was there to start with.

2,880 ml + 120 ml = 3,000 ml

3,000 ml = 3 l

Check it yourself: 3,000 − 2,880 = 120 ✓ The leftover matches the question.

Q2 (c) If 1 l of milk costs ₹40, how much will 3 l milk cost?

3 litres of milk will cost ₹120.

1. Cost of 1 litre = ₹40.
2. We need 3 litres, so multiply.

Page 58 of 63

as e
Class 5 Maths Chapter 8 Weight and Capacity
a g l AglaSem · NCERT Solutions

3. 3 × 40 = ₹120.
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1 l → ₹40
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3 l → 3 × ₹40 = ₹120
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Where the 3 litres came from: Part (b) showed the bottle held exactly 3,000 ml, and
ag
a s emthat same bottle of milk.
3,000 ml = 3 l. So this question is about

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Check it yourself: ₹120 ÷ 3 = ₹40 ✓ back to the price of one litre.
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m A juice vendor has a 5 l container of orange juice. Each glass has a capacity 250
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Q3 (a)

a ml. How many full glasses can he serve before the container becomes empty?

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He can serve 20 full glasses.
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1. Make the units match. The juice is in litres, the glass in millilitres. 5 l = 5 × 1,000 = 5,000 ml.

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2. Name what we need. How many 250 ml glasses fit inside 5,000 ml.

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3. Divide. 5,000 ÷ 250.

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4. Make it easy: four 250 ml glasses make 1,000 ml, that is 1 litre. So each litre gives 4 glasses.
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5. 5 litres
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5 l = 5,000 ml

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1 l = 1,000 ml = 4 glasses of 250 ml
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5 l = 5 × 4 = 20 glasses

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Check it yourself: 20 × 250 ml = 5,000 ml = 5 l ✓ The container empties exactly, with
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nothing left over.

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If he has already served 10 glasses, how much juice is left?
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Q3 (b)

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2,500 ml of juice is left — that is 2 l 500 ml, exactly half the container.

1. Find the juice already served. 10 glasses × 250 ml = 2,500 ml.

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