NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion

NCERT
SOLUTIONS
CLASS - 6TH

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

Class : 6th
Subject : Maths
Chapter : 12
Chapter Name : RATIO AND PROPORTION

Exercise 12.1

Q1 There are 20 girls and 15 boys in a class.
(a) What is the ratio of number of girls to the number of boys?
(b) What is the ratio of number of girls to the total number of students in the class?

Answer. Number of girls = 20
Number of boys = 15
Total number of students = 20 + 15 = 35
(a) Ratio of number of gills to boys = 20/15 = 4/3
(b) Ratio of number of girls to total students = 20/35 = 4/7

Page : 251 , Block Name : Exercise 12.1

Q2 Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis.
Find the ratio of (a) Number of students liking football to number of students liking
tennis. (b) Number of students liking cricket to total number of students.

Answer. Number of students who like football = 6
Number of students who like cricket = 12
Number of students who like tennis = 30 - 6 - 12 = 12
(a) Ratio of the number of students liking football to the number of students liking
tennis = 6/12 = 1/2
(b) Ratio of the number of students liking cricket to the total number of students = 12/30
= 2/5

Page : 251 , Block Name : Exercise 12.1

Q3 See the �gure and �nd the ratio of

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

(a) Number of triangles to the number of circles inside the rectangle. (b) Number of
squares to all the �gures inside the rectangle. (c) Number of circles to all the �gures
inside the rectangle

Answer. Number of triangles = 3
Number of circles = 2
Number of squares = 2
Total number of �gures = 7
(a) Ratio of the number of triangles to the number of circles =3/2
(b) Ratio of the number of squares to all the �gures in the rectangle = 2/7
(c) Ratio of the number of circles to all the �gures in the rectangle = 2/7

Page : 251 , Block Name : Exercise 12.1

Q4 Distances travelled by Hamid and Akhtar in an hour are 9 km and 12 km. Find the
ratio of speed of Hamid to the speed of Akhtar.

Answer. The distance travelled in an hour by a certain object is called the speed of that
object.
Distance travelled by Hamid in one hour = 9 km
Distance travelled by Akhtar in one hour = 12 km
Hamid's speed = 9 km/hr
Akhtars speed = 12 km/hr
Ratio of speed Of Hamid to the speed Of Akhtar = 9/12 = 3/4

Page : 251 , Block Name : Exercise 12.1

Q5 Fill in the following blanks:

Answer.
15
18
= 5×36×3
= 56
5
6
= 56 × 22 = 1012
5
6
= 6 × 5 = 25
5 5
30

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

Therefore, 5, 12, 25 will come in the blanks respectively.
Yes, all these are equivalent ratios.

Page : 251 , Block Name : Exercise 12.1

Q6 Find the ratio of the following :
(a) 81 to 108
(b) 98 to 63
(c) 33 km to 121 km
(d) 30 minutes to 45 minutes

81 3×3×3×3
Answer. (a) 108 = 2×2×3×3×3 = 34
98 14×7
(b) 63 = 9×7
= 14
9
33 3×11 3
(c) 121 = 11×11 = 11
30 2×3×5
(d) 45 = 3×3×5 = 23

Page : 251 , Block Name : Exercise 12.1

Q7 Find the ratio of the following:
(a) 30 minutes to 1.5 hours
(b) 40 cm to 1.5 m
(c) 55 paise to Rs. 1
(d) 500 mL to 2 litres

Answer. (a)
30 min = 3060
= 0.5 hours
0.5 0.5×1
Required ratio = 1.5 = 0.5×3 = 13

(b) 40 cm to 1.5 m
1.5 m = 150 cm
40 4
Required ratio = 150 = 15

(c) 55 paise to Re 1
Re 1 = 100 paise
55 11×5
Required ratio = 100 = 20×5 = 11
20

(d) 500 mL to 2l
1l = 1000 mL
2l = 2000 mL
500 5 5
Required ratio = 2000 = 20 = 5×4 = 14

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

Page : 251 , Block Name : Exercise 12.1

Q8 In a year, Seema earns Rs 1,50,000 and saves Rs 50,000. Find the ratio of a) Money
that Seema earns to the money she saves. (b) Money that she saves to the money she
spends.

Answer. Money earned = Rs 150000
Money saved = Rs 50000
Money spent = Rs 150000 - Rs 50000 = Rs 100000
150000
(a) Ratio of money earned to money saved = 50000 = 31
50000
(b) Ratio of money saved to money spent = 100000 = 12

Page : 251 , Block Name : Exercise 12.1

Q9 There are 102 teachers in a school of 3300 students. Find the ratio of the number of
teachers to the number of students.

102 2×3×17 17
Answer. Ratio required = 3300 = 2×3×550 = 550

Page : 251 , Block Name : Exercise 12.1

Q10 In a college, out of 4320 students, 2300 are girls. Find the ratio of
(a) Number of girls to the total number of students.
(b) Number of boys to the number of girls.
(c) Number of boys to the total number of students.

Answer. Total number of students = 4320
Number of girls = 2300
Number of boys = 4320 - 2300 = 2020
2300 2×2×5×115 115
(a) Required ratio = 4320 = 2×2×5×216 = 216
2020 2×2×5×101 101
(b) Required ratio = 2300 = 2×2×5×115 = 115
2020 2×2×5×101 101
(c) Required ratio = 4320 = 2×2×5×216 = 216

Page : 251 , Block Name : Exercise 12.1

Q11 Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and
remaining opted table tennis. If a student can opt only one game, �nd the ratio of (a)
Number of students who opted basketball to the number of students who opted table
tennis. (b) Number of students who opted cricket to the number of students opting

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

basketball. (c) Number of students who opted basketball to the total number of students.

750
Answer. (a) Required ratio = 250 = 31
800 16
(b) Required ratio = 750 = 15
750 25 5
(c) Required ratio = 1800 = 60 = 12

Page : 252 , Block Name : Exercise 12.1

Q12 Cost of a dozen pens is Rs. 180 and cost of 8 ball pens is Rs. 56. Find the ratio of the
cost of a pen to the cost of a ball pen.

Answer. Cost of a dozen pens = Rs 180
Cost of 1 pen 12 = 180/12 = Rs 15
Cost of 8 ball pens = Rs 56
Cost of a ball pen = 56/8 = Rs 7
Required ratio = 15/7

Page : 252 , Block Name : Exercise 12.1

Q13 Consider the statement: Ratio of breadth and length of a hall is 2 : 5. Complete the
following table that shows some possible breadths and lengths of the hall.

Answer. (i) Length = 50 m
Breadth
50
= 25
5 × Breadth = 50 × 2( By cross-multiplication )
Breadth = 20 m
(ii) Breadth = 40 m
40
Length
= 25
2 × Length = 5 × 40( By cross-multiplication )
Length = 100 m

Page : 252 , Block Name : Exercise 12.1

Q14 Divide 20 pens between Sheela and Sangeeta in the ratio of 3 : 2.

Answer. Terms of 3 : 2 are 3 and 2.

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

Sum of these terms = 3 + 2 = 5
Sheela will get 3/5 of total pens and Sangeeta will get 2/5 of total pens.
Number of pens with Sheela = 35 × 20 = 12
Number of pens with Sangeeta = 25 × 20 = 8

Page : 252 , Block Name : Exercise 12.1

Q15 Mother wants to divide Rs 36 between her daughters Shreya and Bhoomika in the
ratio of their ages. If age of Shreya is 15 years and age of Bhoomika is 12 years, �nd how
much Shreya and Bhoomika will get.

15 5
Answer. Ratio of ages = 12 = 4
Therefore, mother wants to divide Rs 36 in a ratio of 5 : 4.
Terms of 5 : 4 are 5 and 4.
Sum of these terms = 5 + 4 = 9
Shreya will get 5/9 of the total money and Bhoomika will get 4/9 of it.
5
Amount that Shreya will get = 9 × 36 = 20
Amount that Bhoomika will get = 49 × 36 = 16
Therefore, Shreya and Bhoomika will get Rs 20 and Rs 16 respectively.

Page : 252 , Block Name : Exercise 12.1

Q16 Present age of father is 42 years and that of his son is 14 years. Find the ratio of (a)
Present age of father to the present age of son. (b) Age of the father to the age of son,
when son was 12 years old. (c) Age of father after 10 years to the age of son after 10
years.(d) Age of father to the age of son when father was 30 years old.

Answer. (a) Present age of father = 42 years
Present age of son = 14 years
Required ratio = 42/14 = 3/1
(b) Two years ago, the age of the son was 12 years and the age of the father was 42 —
2 = 40 years
40 4×10 10
Required ratio = 12 = 4×3 = 3
(c) After 10 years, the age of the father and son will be 52 years and 24 years
respectively.
52 4×13 13
Required ratio = 24 = 4×6 = 6
(d) 12 years ago, the father was 30 years old.
At that time, age of son 14 - 12 = 2 years
30 2×15 15
Required ratio = 2 = 2 = 1

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

Page : 252 , Block Name : Exercise 12.1

Exercise 12.2

Q1 Determine if the following are in proportion. (a) 15, 45, 40, 120 (b) 33, 121, 9,96 (c)
24, 28, 36, 48 (d) 32, 48, 70, 210 (e) 4, 6, 8, 12 (f) 33, 44, 75, 100

15 40
Answer. (a) 45 = 13 , 120 = 13
Therefore, 15 : 45 = 40 : 120
Hence, these are in proportion.
33 3 9 3
(b) 121 = 11 , 96 = 32
Therefore, 33 : 121 ≠ 9 : 96
Hence, these are not in proportion.
(c) 24
28
= 67 , 36
48
= 34
Therefore, 24 : 28 ≠ 36 : 48
Hence, these are not in proportion.
32 70
(d) 48 = 23 , 210 = 13
Therefore, 32 : 48 ≠ 70 : 210
Hence, these are not in proportion.
8
(e) 46 = 23 , 12 = 23
Therefore, 4 : 6 = 8 : 12
Hence, these are in proportion.
75
(f) 33
44
= 34 , 100 = 34
Therefore, 33 : 44 = 75 : 100
Hence, these are in proportion.

Page : 255 , Block Name : Exercise 12.2

Q2 Write True ( T ) or False ( F ) against each of the following statements : (a) 16 : 24 :: 20
: 30 (b) 21: 6 :: 35 : 10 (c) 12 : 18 :: 28 : 12 (d) 8 : 9 :: 24 : 27 (e) 5.2 : 3.9 :: 3 : 4 (f) 0.9 :
0.36 :: 10 : 4

16 20
Answer. (a) 24 = 23 , 30 = 23
Therefore, 16 : 24 = 20 : 30
Hence, True
(b) 21
6
= 72 , 35
10
= 72

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

Therefore, 21 : 6 = 35 : 10
Hence, True
(c) 12
18
= 23 , 28
12
= 73
Therefore, 12 : 18 ≠ 28 : 12
Hence, False
(d) 24
27
= 3×8
3×9
= 89
T herefore, T rue
5.2
(e) 3.9 = 43
Therefore, 5.2 : 3.9 ≠ 3 : 4
Hence, False
0.9 90 10
(f) 0.36 = 36 = 4
Therefore, 0.9 : 0.36 = 10 : 4
Hence, True

Page : 255 , Block Name : Exercise 12.2

Q3 Are the following statements true? (a) 40 persons : 200 persons = Rs 15 : Rs 75 (b) 7.5
litres : 15 litres = 5 kg : 10 kg (c) 99 kg : 45 kg = Rs 44 : Rs 20 (d) 32 m : 64 m = 6 sec : 12
sec (e) 45 km : 60 km = 12 hours : 15 hours

40 15
Answer. (a) 200 = 15 , 75 = 15
True
7.5 5
(b) 15 = 12 , 10 = 12
True
99
(c) 45 = 11 , 44 = 11
5 20 5
True
32 6
(d) 64 = 12 , 12 = 12
True
45
(e) 60 = 34 , 12
15
= 45
False

Page : 256 , Block Name : Exercise 12.2

Q4 Determine if the following ratios form a proportion. Also, write the middle terms and
extreme terms where the ratios form a proportion. (a) 25 cm : 1 m and Rs 40 : Rs 160
(b)39 litres : 65 litres and 6 bottles : 10 bottles (c) 2 kg : 80 kg and 25 g : 625 g (d) 200 mL
: 2.5 litre and Rs 4 : RS 50

Answer. (a)

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

25
25cm = 100 m
0.25 40
1
= 14 and 160 = 14
Yes. These are in proportion.
Middle terms are 1 m, Rs 40.
Extreme terms are 25 cm, Rs 160.

(b)
39 6
65
= 35 and 10 = 35
Yes. These are in proportion.
Middle terms are 65 l, 6 bottles
Extreme terms are 39 l, 10 bottles.

(c)
1l = 1000mL
2.5l = 2500mL
200 2 4 2
2500
= 25 and 50 = 25
Yes. These are in proportion
Middle terms are 2.5 l, Rs 4.
Extreme terms are 20 mL, Rs 50.

Page : 256 , Block Name : Exercise 12.2

Exercise 12.3

Q1 If the cost of 7 m of cloth is Rs 1470, �nd the cost of 5 m of cloth.

Answer. Cost of 7 m cloth = Rs 294
294
Cost of 1 m cloth = 7 = Rs 42
Therefore, cost of 5 m cloth = 42 x 5 = Rs 210

Page : 259 , Block Name : Exercise 12.3

Q2 Ekta earns Rs 3000 in 10 days. How much will she earn in 30 days?

Answer. Money earned in 10 days = Rs 1500
1500
Money earned in 1 day = 10 = Rs 150
Therefore, money earned in 30 days = 150 x 30 = Rs 4500

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

Page : 259 , Block Name : Exercise 12.3

Q3 If it has rained 276 mm in the last 3 days, how many cm of rain will fall in one full
week (7 days)? Assume that the rain continues to fall at the same rate.

Answer. Measure of rain in 3 days = 276 mm
276
Measure of rain in 1 day = 3 = 92mm
Therefore, measure of rain in 7 days = 92 x 7 = 644 mm

Page : 259 , Block Name : Exercise 12.3

Q4 Cost of 5 kg of wheat is Rs 91.50. (a) What will be the cost of 8 kg of wheat? (b) What
quantity of wheat can be purchased in Rs 183?

Answer. (a) Cost of 5 kg wheat = Rs 30.50
30.50
Cost of 1 kg wheat = 5 = Rs 6.10
Therefore, cost of 8 kg wheat = 6.10 × 8 = Rs48.80
(b) Wheat purchased in Rs 30.50 = 5 kg
5
Wheat purchased in Re 1 = 30.50 kg
5
Therefore, wheat purchased in Rs 61 = 30.50 × 61 = 10kg

Page : 259 , Block Name : Exercise 12.3

Q5 The temperature dropped 15 degree celsius in the last 30 days. If the rate of
temperature drop remains the same, how many degrees will the temperature drop in the
next ten days?

Answer. Temperature drop in 30 days = 15∘ C
∘
Temperature drop in 1 day = 30 = ( 12 ) C
15

Thus, there will be a temperature drop in next 10 days = 12 × 10 = 5∘ C
Thus, there will be temperature drop of 5∘ C in the next ten days.

Page : 259 , Block Name : Exercise 12.3

Q6 Shaina pays Rs 15000 as rent for 3 months. How much does she has to pay for a whole
year, if the rent per month remains same?

Answer. Rent for 3 months = Rs 7500
Rent for 1 month = 7500/3 = Rs 2500

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

Therefore, rent for 12 months= 25 00 x 12 = 30000
Thus, she has to pay Rs 30000 for a whole year.

Page : 259 , Block Name : Exercise 12.3

Q7 Cost of 4 dozen bananas is Rs 180. How many bananas can be purchased for Rs 90?

Answer. Numbers of bananas bought in Rs 60 = 4 dozens = 4 x 12 = 48
Number of bananas bought in Re 1 = 48/60
48
Therefore, number of bananas bought in Rs 12.50 = 60 × 12.50 = 10 bananas
Thus, 10 bananas can be purchased for Rs 12.50.

Page : 259 , Block Name : Exercise 12.3

Q8 The weight of 72 books is 9 kg. What is the weight of 40 such books?

Answer. Weight of 72 books = 9 kg
Weight of 1 book = 9/72 = 1/8 kg
Therefore, weight of 40 books = 1/8 x 40 = 5 Kg
Thus, the weight of 40 such books is 5 kg.

Page : 259 , Block Name : Exercise 12.3

Q9 A truck requires 108 litres of diesel for covering a distance of 594 km. How much
diesel will be required by the truck to cover a distance of 1650 km?

Answer. Diesel required for 594 km = 108 litres
Diesel require for 1 km = 108/594 = 2/11 litre
Therefore, diesel required for 1650 km = 2/11 x 1650 = 300 litres
Thus, 300 litres diesel will be required by the truck to cover a distance of 1650 km.

Page : 259 , Block Name : Exercise 12.3

Q10 Raju purchases 10 pens for Rs 150 and Manish buys 7 pens for Rs 84. Can you say
who got the pens cheaper?

Answer. Raju purchased 10 pens for Rs 150.
∴ Price of 1 pen = 150/10 = Rs 15
Manish purchased 7 pens for Rs 84.
∴ Price of 1 pen = 84/7 = Rs 12
Therefore, manish got the pens cheaper.

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Book: Mathematics NCERT Solutions | Chapter - 12 Maths

Page : 259 , Block Name : Exercise 12.3

Q11 Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more
runs per over?

Answer. Runs made by Anish in 6 overs = 42
∴ Runs made by Anish in 1 over = 42/6 =7
Runs made by Anup in 7 overs = 63
∴ Runs made by Anup in 1 over = 63/7 = 9
Clearly, Anup made more runs per over.

Page : 259 , Block Name : Exercise 12.3

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