NCERT Solutions Class 5 Maths Chapter 12 Racing Seconds

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 12: Racing Seconds

NCERT Textbook — Math Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

155 – 163 12 53 English

Solutions, notes, sample papers & more at 48 pages

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

CLASS 5 · MATHS · MATH MELA

NCERT Solutions — Chapter 12: Racing Seconds
Chapter 12 of Math Mela is about time. Raghav's morning yoga, a 200 m walking race at school, and a set of
wall clocks bring in a brand new unit — the second. The chapter teaches you to read a clock with three hands,
to write the same time in the 12-hour and the 24-hour way, to change hours into minutes and minutes into
seconds, and to work out how long something took. The big idea: time is counted in sixties, not in tens.

TEXTBOOK BOOK PAGES

Math Mela (Class 5) 155 – 163

SECTIONS QUESTIONS

12 53

MEDIUM

English

Let us find out — Page 155
Raghav's yoga clocks, time elapsed, and the painting table

LET US FIND OUT

Q1 At what time did Raghav start practising Yoga?

Raghav started at 05:35 a.m. That is 25 minutes before six in the morning.
Look at the first picture in your book. Raghav is standing with folded hands, and the clock
behind him is the one to read.

Page 1 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

12
11 1
10 2
9 3

8 4
7 5
6

05:35 a.m.
The blue short hand is the hour hand. The green long hand is the minute hand. This is the clock in the
first picture.

Here is how to read any clock, step by step.

1. Find the short thick hand. This is the hour hand. In the picture it lies between 5 and 6. It
has already passed 5, so the hour is 5.
2. Find the long hand. This is the minute hand. It is pointing at 7.
3. Change that number into minutes. Each big number stands for 5 minutes. So count in
fives up to 7: 5, 10, 15, 20, 25, 30, 35.
4. Put the two together. Hour 5 and 35 minutes gives 5:35.
5. Is it a.m. or p.m.? The book says Raghav practises yoga in the morning, so it is a.m.

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Hour hand → between 5 and 6 → hour = 5

Minute hand → on 7 → 7 × 5 = 35 minutes

Time = 05:35 a.m.

Tip: Never read the minute hand as the number it points to. It points at 7, but that
means 35 minutes, not 7 minutes. Always multiply by 5.

Q2 At what time did he finish?

Raghav finished at 05:55 a.m. — five minutes before six.
The second picture shows him sitting in yoga posture. Read the clock on that wall the same way.

Page 3 of 48

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Class 5 Maths Chapter 12 Racing Seconds
a g l AglaSem · NCERT Solutions

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The minute hand has moved on to 11. The hour hand is still between 5 and 6, so the hour has not
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1. Short hand: still between 5 and 6, so the hour is 5.
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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Why the hour hand hardly moved: The hour hand takes a whole hour to travel
from one number to the next. In 20 minutes it creeps only one-third of that gap.
That is why it still sits between 5 and 6.

Q3 How much time did he spend practising Yoga?

He practised for 20 minutes.
We know he began at 05:35 a.m. and stopped at 05:55 a.m. We have to find the gap between
the two times.

12 12
11 1 11 1
10 2 10 2
20 minutes
9 3 9 3
8 4 8 4
7 5 7 5
6 6

Start 05:35 a.m. Finish 05:55 a.m.

hour minute second

The minute hand travels from 7 to 11 — four big steps of 5 minutes each.

1. The hour is the same in both clocks — 5 both times. So no hours have passed at all.
2. Count only the minutes. Start minute = 35. Finish minute = 55.
3. Subtract: 55 − 35 = 20.

Finish time = 05 : 55

Start time = 05 : 35

Difference = 00 : 20
Raghav practised yoga for 20 minutes

Page 5 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Check it yourself: Count the big steps of the minute hand instead. 7 → 8 → 9 → 10
→ 11 is 4 steps, and each step is 5 minutes. 4 × 5 = 20 minutes. Same answer.

Q4 (a) Find the time elapsed between the given time periods. Share your strategies. (a)
01:15 p.m. to 01:42 p.m.?

27 minutes.
Time elapsed means how much time went by from the first time to the second time.

1. Compare the hours. Both times are 01, so the hour has not changed. Nothing to do here.
2. Compare the minutes. We go from 15 minutes to 42 minutes.
3. Subtract the minutes: 42 − 15 = 27.

01 : 42 (later time)

01 : 15 (earlier time)

─────────

00 : 27 → 27 minutes

Another strategy (jumping forward): From 01:15 jump 5 minutes to 01:20. From
01:20 jump 20 minutes to 01:40. From 01:40 jump 2 minutes to 01:42. Now add the
jumps: 5 + 20 + 2 = 27 minutes. Same answer, and you can do it in your head.

Q4 (b) Find the time elapsed between the given time periods. (b) 03:18 p.m. to 08:18
p.m.?

5 hours.

1. Look at the minutes first. Both times show 18 minutes. They are the same, so no extra
minutes are involved.
2. Now the hours. We go from 3 o'clock to 8 o'clock.
3. Subtract: 8 − 3 = 5.

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

08 : 18 (later time)

03 : 18 (earlier time)

─────────
05 : 00 → 5 hours

Count it on your fingers: 3 to 4, 4 to 5, 5 to 6, 6 to 7, 7 to 8. That is 5 hops of one
hour each — 5 hours. Both times are p.m., so this is one afternoon-to-evening
stretch, not a whole day.

Q4 (c) Find the time elapsed between the given time periods. (c) 09:15 a.m. to 11:30
a.m.?

2 hours 15 minutes.
The best way here is to move in two easy hops — first the whole hours, then the leftover
minutes.

1. Hop 1 — whole hours. From 09:15 a.m. to 11:15 a.m. is 2 hours. (Keep the minutes
unchanged while you do this.)
2. Hop 2 — the extra minutes. From 11:15 a.m. to 11:30 a.m. is 15 minutes, because 30 − 15 =
15.
3. Add the two hops. 2 hours + 15 minutes = 2 hours 15 minutes.

09:15 a.m. → 11:15 a.m. = 2 hours

11:15 a.m. → 11:30 a.m. = 15 minutes

Time elapsed = 2 hours 15 minutes

Why hop in two steps: Time is not counted in tens. If you write 11:30 above 09:15
and subtract like ordinary numbers you can easily get muddled when the minutes
do not go. Hopping forward keeps the hours and the minutes apart, so nothing gets
mixed up.

Page 7 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Check it yourself: Walk the hops forwards again. Start at 09:15 a.m., add 2 hours →
11:15 a.m., add 15 minutes → 11:30 a.m. That is exactly the time we were given, so
the answer is right ✓

Q5 (a) The table below shows the time taken by 3 children to paint a picture.

NAME TIME TAKEN

Raghav 1 hour 20 minutes

Rani 2 hours 10 minutes

Ritu 1 hour 35 minutes

Page 155, Question 5 — the table printed in the book.

(a) Who took the longest time?

Rani took the longest time — 2 hours 10 minutes.
To compare times fairly, change them all into the same unit. Minutes are the easiest here.
Remember: 1 hour = 60 minutes.

1. Raghav: 1 hour 20 minutes = 60 + 20 = 80 minutes.
2. Rani: 2 hours 10 minutes = 60 + 60 + 10 = 130 minutes.
3. Ritu: 1 hour 35 minutes = 60 + 35 = 95 minutes.
4. Compare: 130 > 95 > 80.

NAME TIME TAKEN IN MINUTES POSITION

Raghav 1 hour 20 minutes 80 min Fastest

Rani 2 hours 10 minutes 130 min Slowest

Ritu 1 hour 35 minutes 95 min In between

Longest time = 130 minutes = Rani (2 hours 10 minutes)

Page 8 of 48

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Class 5 Maths Chapter 12 Racing Seconds
a g l AglaSem · NCERT Solutions

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Tip: You could also compare without any working here. Rani is the only one who

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took more than 2 hours, and the others took less than 2 hours. So Rani is clearly the
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Q5 (b)

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NAME
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TIME TAKEN

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Raghav 1 hour 20 minutes

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Rani 2 hours 10 minutes

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Ritu 1 hour 35 minutes

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Raghav took the least time — 1 hour 20 minutes.

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= 80 minutes

Ritu = 95 minutes
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Rani = 130 minutes
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1. Raghav and Ritu both took 1 hour and a bit, so one of them must be the quickest.
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2. Raghav's extra bit is 20 minutes. Ritu's extra bit is 35 minutes.
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3. 20 minutes is less than 35 minutes, so Raghav finished first.

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ag How much quicker? 95 − 80 = 15. Raghav finished 15 minutes before Ritu, and 130
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Let us find out (continued) — Page 156

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

12-hour format and 24-hour format

LET US FIND OUT

Q6 Fill in the blanks by writing the time in the appropriate format. 05:30 a.m. — 05:30
hours; ………… — 08:35 hours; 11:55 a.m. — ……… hours; 02:30 p.m. — 14:30 hours;
05:30 p.m. — ……… hours; 09:35 p.m. — ……… hours.

Here is the completed table. The two filled rows the book gives us show exactly what to do.

TIME IN 12-HOUR FORMAT TIME IN 24-HOUR FORMAT

05:30 a.m. 05:30 hours

08:35 a.m. 08:35 hours

11:55 a.m. 11:55 hours

02:30 p.m. 14:30 hours

05:30 p.m. 17:30 hours

09:35 p.m. 21:35 hours

The rule, in two lines:

1. a.m. time → write the same numbers, just say hours instead of a.m. Nothing changes.
2. p.m. time → add 12 to the hour. The minutes never change.

08:35 hours is before 12, so it is morning → 08:35 a.m.

11:55 a.m. is morning → 11:55 hours

05:30 p.m. → 5 + 12 = 17 → 17:30 hours

09:35 p.m. → 9 + 12 = 21 → 21:35 hours

Why we add 12: A full day is 24 hours long, but a clock face has only 12 numbers. So
the same 12 numbers get used twice in a day. The 24-hour way does not reuse them
— it keeps counting: after 12 noon comes 13, 14, 15 and so on up to 23. Every p.m.
hour is 12 hours after its a.m. twin, so we add 12.

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Where you have seen this: Look at a railway ticket or the board at a bus stand. A
train at 17:30 hours is a train at 5:30 in the evening. Nobody has to ask whether it is
morning or evening — that is the whole point of the 24-hour format.

Q7 Match the following. Time in 12-hour format: 06:30 a.m., 08:45 p.m., 11:45 p.m., 04:30
a.m., 07:30 p.m., 01:30 a.m. Time in 24-hour format: 01:30 hours, 23:45 hours, 06:30
hours, 20:45 hours, 04:30 hours, 19:30 hours.

Here are the six correct pairs.

12-HOUR FORMAT WORKING 24-HOUR FORMAT

06:30 a.m. morning, so no change 06:30 hours

08:45 p.m. 8 + 12 = 20 20:45 hours

11:45 p.m. 11 + 12 = 23 23:45 hours

04:30 a.m. morning, so no change 04:30 hours

07:30 p.m. 7 + 12 = 19 19:30 hours

01:30 a.m. after midnight, so no change 01:30 hours

A quick way to match without any working:

1. Every a.m. time matches the 24-hour time with the same digits. Spot those first: 06:30,
04:30 and 01:30.
2. The three left over must be the p.m. ones. Their 24-hour hours are all bigger than 12: 20, 23
and 19.
3. Match each by subtracting 12: 20 − 12 = 8, so 20:45 goes with 08:45 p.m. 23 − 12 = 11, so
23:45 goes with 11:45 p.m. 19 − 12 = 7, so 19:30 goes with 07:30 p.m.

Careful with 01:30 a.m.: This is half past one at night, just after midnight — not in
the afternoon. In the 24-hour format it stays 01:30 hours. Midnight itself is written
00:00 hours.

School Race — Page 157

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Seconds — a new and smaller unit of time

SCHOOL RACE

Q1 Do you notice the use of a new unit ‘seconds’ in the picture?

200 m 1
2 Min. Sec.

01:55 3
Min. Sec.
Min. Sec.
01:56
01:57

Page 156, “School Race” — the winners’ stand after the 200 m walking race. Each board
shows the time in minutes and seconds.

Yes. The three little boards on the winners' podium say Min. Sec. at the top. So each timing is
given in minutes and seconds, not in hours and minutes.
Read the three boards in your book:

PODIUM PLACE BOARD SHOWS MEANS

1 01 : 55 1 minute 55 seconds

2 01 : 56 1 minute 56 seconds

3 01 : 57 1 minute 57 seconds

The book's new fact: 1 min = 60 seconds

Page 12 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Why a race needs seconds: All three girls took about one minute. If we only said 1
minute for each of them, we could never tell who won. Seconds are small enough to
show the tiny gaps between them. A smaller unit gives a more exact measurement.

How long is a second? Say one thousand one slowly. That is about one second. Your
heart beats roughly once every second when you are sitting quietly.

Q2 In situations like a race, ‘seconds’ help us observe small differences in time taken by
participants. Each participant took 1 minute but how much more?

Each girl took 1 full minute and then some extra seconds — 55, 56 and 57 seconds more.

1. Split each timing into two parts. The number before the colon is minutes; the number
after it is seconds.
2. 01 : 55 → 1 minute + 55 seconds more.
3. 01 : 56 → 1 minute + 56 seconds more.
4. 01 : 57 → 1 minute + 57 seconds more.

If you want the whole time in seconds, change the 1 minute into 60 seconds and add.

1 min 55 s = 60 + 55 = 115 seconds
1 min 56 s = 60 + 56 = 116 seconds

1 min 57 s = 60 + 57 = 117 seconds

How close the race was: 116 − 115 = 1 second, and 117 − 116 = 1 second. Only one
second separated each girl from the next. That is less time than it takes you to say
her name.

Q3 Identify the child who won the race. How much time did the child take?

The girl standing on box number 1 won the race. She is the one in the red T-shirt with her fist
raised and the gold medal round her neck. She took 1 minute 55 seconds.

1. In a race, the winner is the one who takes the least time — not the most.

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Class 5 Maths Chapter 12 Racing Seconds
a g l AglaSem · NCERT Solutions

2. Compare the three timings: 1 min 55 s, 1 min 56 s, 1 min 57 s.
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3. All three have the same 1 minute, so compare only the seconds: 55, 56, 57.
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4. 55 is the smallest, so that girl finished first.

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= 60 s + 55 s = 115 seconds
. co ag
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Note about the names: The book
Mary, but the picture does not print a name on any girl. So we can say which place

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each timing belongs to, but not which name. Look at the picture in your own book
and decide with your class who is who.
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Try
200 m walking race, 2 seconds is only a couple of steps.

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Let Us Do — Page 157 a g
Seconds or minutes? Tick the right cell

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LET US DO

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m Estimate whether you would take seconds or minutes to complete the following
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Q1

ag activities. Tick the appropriate cell. (Blinking of eyes; Switching on and switching off

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the lights; Counting from 1–20; Filling a glass from the tap; Melting of an ice-cube;

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Making a phone call; Sitting down on the floor; Drinking a glass of water; Snapping
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fingers; Washing hands)

ANSWER agl

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Here is the table with a tick in the sensible cell for each activity, and a rough time so you can see
why.
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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

ACTIVITY SECONDS MINUTES ABOUT HOW LONG

Blinking of eyes ✓ less than 1 second

Switching on and switching off the lights ✓ about 2 seconds

Counting from 1–20 ✓ about 15 seconds

Filling a glass from the tap ✓ about 10 seconds

Melting of an ice-cube ✓ 15 minutes or more

Making a phone call ✓ a few minutes

Sitting down on the floor ✓ about 3 seconds

Drinking a glass of water ✓ about 10 seconds

Snapping fingers ✓ less than 1 second

Washing hands ✓ about 20–30 seconds

How to decide, for any activity:

1. Picture yourself doing it once. Do it slowly in your mind.
2. Ask: could I count it out while holding my breath? If yes, it is a job for seconds.
3. Ask: would I get bored waiting? If yes, it is a job for minutes.
4. Then check with a clock that has a seconds hand, or with a stopwatch.

Why only two answers are ‘minutes’: Melting an ice cube and making a phone call
are the only two things on the list you cannot finish in one breath. Everything else on
the list is over before the seconds hand has gone even half way round.

Check it yourself: Ask a friend to watch the seconds hand while you wash your
hands properly with soap. Most people take 20 to 30 seconds. If you take longer
than 60 seconds, then for you it becomes a minutes job — measuring is allowed to
give different answers for different people.

In-text Questions — Page 158

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Your own list, and how many you can do in a minute

WRITE IN THE BOX

Q1 List events other than the ones listed above that you can do or that can happen in
less than a minute or in a few seconds.

Write your own list on the dotted lines in the book. Anything you can finish before the seconds
hand goes once round belongs here.
How to make a good list:

1. Walk through your own day — waking up, school, playground, kitchen, evening.
2. For each thing you remember, ask: can I finish it in less than one minute?
3. Keep it only if the answer is yes.
4. Try one or two of them with a clock and see if you were right.

Sample answer:

Tying my shoelaces — about 20 seconds
Sharpening a pencil — about 15 seconds
Clapping 20 times — about 10 seconds
Writing my full name — about 10 seconds
Opening my school bag and taking out a book — about 8 seconds
Drinking a glass of buttermilk — about 20 seconds
A phone ringing before someone picks it up — about 10 seconds
An auto passing the school gate — about 3 seconds
Lighting a diya — about 5 seconds
A cricket bowler running in and bowling one ball — about 12 seconds
Sneezing — less than 1 second
Switching off a fan — about 2 seconds

Try This: Find one thing that takes almost exactly one minute. Boiling an egg does
not (that takes minutes and minutes), but brushing one side of your teeth might.
Time it and see.

Page 16 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Q2 Estimate and verify how many of these you can do in a minute. (Number of balloons
blown; Number of push-ups; Number of breaths; Number of hops on one leg)

This one you must actually do — first guess, then measure. The guess is called an estimate. The
count you get after doing it is the actual number.
Method:

1. Write your guess first. Fill the whole Estimated Number column before you begin. Guessing
after measuring is not estimating.
2. Ask a friend to be the timekeeper. They watch a clock with a seconds hand and say start
and stop. One minute = the seconds hand going once all the way round.
3. Do the activity steadily for one minute while the friend counts aloud.
4. Write the count in the Actual Number column.
5. Compare. Was your guess close? Then swap places and let your friend try.

Sample answer (this is what one Class 5 student got — yours will be different, and that is fine):

ACTIVITY ESTIMATED NUMBER ACTUAL NUMBER

Number of balloons blown 4 3

Number of push-ups 20 14

Number of breaths 25 18

Number of hops on one leg 50 62

Why guesses are usually too high: Things that are easy for a few seconds get tiring
long before the minute is over. Push-ups and blowing balloons slow you down.
Hopping is light work, so there the real number can even beat the guess.

Did you know? A resting person breathes about 18 to 20 times in a minute. Run
around the ground first and count again — the number goes up, because your body
needs more air.

Let Us Find — Page 158

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Three things to measure with a seconds hand

LET US FIND

Q1 Find out the number of times you can skip the rope in 10 seconds.

You have to measure this one yourself. Here is exactly how.

1. Fix the 10 seconds. A friend watches the seconds hand. Ten seconds is two big steps of the
seconds hand — for example from 12 to 2.
2. Get ready with the rope behind your feet before the timing starts.
3. On start, skip steadily and count each time the rope passes under your feet.
4. On stop, write down your count.
5. Do it three times and take the best count. Practice makes the number go up.

Sample answer: I skipped 18 times in 10 seconds.

18 skips in 10 seconds

In 60 seconds (1 minute) that would be about 6 × 18 = 108 skips

Why we multiply by 6: One minute is 60 seconds, and 60 ÷ 10 = 6. So a minute
holds six lots of 10 seconds. Six lots of 18 skips is 108 skips — as long as you do not
get tired, which you probably will.

Q2 How long does it take you to write the word FRIEND?

Time yourself with a clock that has a seconds hand.

1. Keep your pencil and notebook ready, page open.
2. A friend says start when the seconds hand touches 12.
3. Write FRIEND in your normal handwriting — not scribbled, not extra neat.
4. Say done. Your friend reads how many small marks the seconds hand has moved.

Sample answer: I took 5 seconds to write FRIEND in capital letters.

FRIEND has 6 letters

6 letters in 5 seconds → a little under 1 second per letter

Page 18 of 48

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Class 5 Maths Chapter 12 Racing Seconds
a g l AglaSem · NCERT Solutions

co m
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Try This: Now write FRIEND ten times and time that. Did it take ten times as long, or

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less? Most children speed up after the first two or three tries.

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Q3 How long does it take you to run 100m?

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agwith a friend or your teacher holding the watch.
Measure this on your school ground,

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1. Mark the 100 m with a starting line and a finishing line. Ask your teacher to help measure it.
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2. The timekeeper stands at the finish line, watching the seconds hand.

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3. The timekeeper notes the second at which you start.
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4. The timekeeper notes the second at which you cross the finish line.

a gl5.aSubtract to get your time.
Sample answer: I started when the seconds hand was on 12 and finished when it had moved
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21 small marks. So I took 21 seconds to run 100 m.

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a
Why we time the runner, not the distance: The distance is fixed at 100 m for
everybody. So the only thing that can change is the time. Whoever takes the fewest
seconds is the fastest — the same rule that decided the 200 m walking race on page
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157.
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m you know? The fastest men in the world run 100 m in under 10 seconds. That is
a s eDid
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Let Us Do — Page 159
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Observe the clocks and fill in the blanks

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LET US DO

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m .c Observe the clocks and fill in the blanks. (1) Rani took
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bed.

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Rani took 30 seconds.
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Both clocks have three hands. Only the thin red seconds hand has moved, so we only have to
look at that one.

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

12 12
11 1 11 1
10 2 10 2
30 seconds
9 3 9 3
8 4 8 4
7 5 7 5
6 6

Rani gets up Rani is out of bed

hour minute second

Left clock: 6:45 and 0 seconds. Right clock: 6:45 and 30 seconds. Only the red hand has shifted.

1. First clock. The red hand is on 12. That means 0 seconds.
2. Second clock. The red hand is on 6. Count in fives from 12: 5, 10, 15, 20, 25, 30. So 30
seconds.
3. Subtract. 30 − 0 = 30.

End reading = 30 seconds
Start reading = 0 seconds

Time taken = 30 − 0 = 30 seconds

Tip: On the seconds hand, each big number is worth 5 seconds, exactly like the
minute hand. 12 → 0 s, 3 → 15 s, 6 → 30 s, 9 → 45 s. Half a round is 30 seconds.

Q2 (2) Raghav took ______ sec. to move from his room to the kitchen.

Raghav took 35 seconds.

Page 20 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

12 12
11 1 11 1
10 2 10 2
35 seconds
9 3 9 3
8 4 8 4
7 5 7 5
6 6

Leaves his room Reaches the kitchen

hour minute second

Left clock: 4:45 and 0 seconds. Right clock: 4:45 and 35 seconds.

1. First clock: red hand on 12 → 0 seconds.
2. Second clock: red hand on 7. Count in fives: 5, 10, 15, 20, 25, 30, 35. So 35 seconds.
3. Subtract: 35 − 0 = 35.

35 seconds − 0 seconds = 35 seconds

Why the minute hand did not move: The minute hand shifts to the next small mark
only after a whole 60 seconds. Raghav took just 35 seconds, so the seconds hand
had not finished its round yet and the green hand stayed on 9.

Q3 (3) Ritu took ______ sec. to pick up a piece of paper from the floor.

Ritu took 15 seconds.
This one is different — the seconds hand crosses the 12 while she is bending down, so read it
carefully.

Page 21 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

12 12
11 1 11 1
10 2 10 2
15 seconds
9 3 9 3
8 4 8 4
7 5 7 5
6 6

Ritu bends down Paper picked up

hour minute second

Left clock: the red hand is on 9, which is 45 seconds. Right clock: the red hand is back on 12, which is
a full 60 seconds.

1. First clock: red hand on 9. Count in fives: 5, 10, 15, 20, 25, 30, 35, 40, 45. So 45 seconds.
2. Second clock: red hand on 12. It has gone all the way round to the end of that minute, so
this is 60 seconds.
3. Subtract: 60 − 45 = 15.

60 seconds − 45 seconds = 15 seconds

Why we call the second reading 60 and not 0: The red hand did not stand still — it
carried on from 45 to the top of the dial. Those last marks are 46, 47, 48 … right up
to 60. Once it touches 12 the minute is complete, and only then does the counting
start again from 0.

Count it another way: From 9 to 10 is 5 seconds, 10 to 11 is 5 seconds, 11 to 12 is 5
seconds. 5 + 5 + 5 = 15 seconds.

Q4 (4) Raghu took ______ sec. to wash his spoon and plate.

Raghu took 60 seconds, that is 1 whole minute.

Page 22 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

At first the two clocks look exactly the same — the red hand is on 5 in both. The clue is hidden in
the green minute hand.

12 12
11 1 11 1
10 2 10 2
60 seconds
9 3 9 3
8 4 8 4
7 5 7 5
6 6

Raghu starts washing Raghu finishes

hour minute second

The red hand is on 5 in both clocks. But look at the green minute hand — it has slipped forward by
one small mark.

1. First clock: green hand on 12, red hand on 5 → 25 seconds past six o'clock.
2. Second clock: the red hand is again on 5, so again 25 seconds. But the green hand has
moved on by one small mark.
3. What one small mark means. The minute hand moves one small mark only when the
seconds hand has gone once fully round.
4. So the seconds hand made one full round. One full round = 60 seconds.

One full round of the seconds hand = 60 seconds = 1 minute

Raghu took 60 seconds

Why the seconds hand alone is not enough: The seconds hand comes back to the
same place every single minute. So the same red position can mean 25 seconds, or 1
minute 25 seconds, or 2 minutes 25 seconds. To know how many whole minutes
have gone, you must look at the minute hand as well.

Page 23 of 48

as e
Class 5 Maths Chapter 12 Racing Seconds
a g l AglaSem · NCERT Solutions

co m
m.
Check it yourself: Count the seconds hand's journey — 25 → 30 → 45 → 60 → 0 →

m as e
l
25. That is 35 seconds to reach the top and 25 seconds after it. 35 + 25 = 60 seconds

m .co a g
se
✓

g l a
a
om 160
Draw the Missing Seconds Hand — Page
.c ag
s e m
a
Add the red hand to the clock on the right

LET US DO agl

co m
e m.
Draw the missing seconds hand on the clocks on the right side. (1) Raghu took 20

as
Q1

m l
.co
sec. to read a sentence in his book.
a g
se m
g l a
a Draw the seconds hand pointing at 4.

m a s
m .co agl
l a se
a g
12 12
m
.co 2
11 1 11 1
10 2
se
10 m
com9 9gla
20 seconds later

m. a
3 3
as e
a g l 8 4 8 4
7 5 7 5
6 6
se m
com g l a
m . a
gl
Clock in the book ase Draw the red hand here
a
hour minute second
. com
m a s emlands it on the 4.
co gl
The seconds hand starts at 12 and moves 20 seconds forward, which

. a
as em
agl
1. Read the left clock. The red seconds hand is on 12, so the start reading is 0 seconds.
2. Add the time taken. 0 + 20 = 20 seconds.
.c
s e m
m a
agl
3. Turn 20 seconds into a number on the dial. Each big number is 5 seconds, so divide: 20 ÷ 5

. co
m
= 4.

as e
l
4. Draw a thin hand from the centre to the 4. Make it the longest hand on the dial.
a g

co m
m .
m ase
.co


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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Start = 0 s, time taken = 20 s

0 + 20 = 20 seconds

20 ÷ 5 = the number 4 on the dial

Tip: The seconds hand is always drawn thinnest and longest. If your hand is short
and fat, it will look like the hour hand.

Q2 (2) Rani took 30 sec. to color a rectangle.

Draw the seconds hand pointing at 6 — straight down.

12 12
11 1 11 1
10 2 10 2
30 seconds later
9 3 9 3
8 4 8 4
7 5 7 5
6 6

Clock in the book Draw the red hand here

hour minute second

Half a round of the dial is 30 seconds, and half a round from 12 lands on 6.

1. Left clock: red hand on 12 → start reading 0 seconds.
2. Add: 0 + 30 = 30 seconds.
3. Find the number: 30 ÷ 5 = 6.
4. Draw the thin hand straight down to the 6.

Page 25 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

30 seconds = 30 ÷ 5 = the number 6

30 seconds is also half a minute, because 60 ÷ 2 = 30

Picture it: Half of the round dial is 30 seconds, a quarter of it is 15 seconds, and
three quarters is 45 seconds. Learn these three and you can read a seconds hand at
a glance.

Q3 (3) Raghav took 60 sec. to move from his home to the garden.

Draw the seconds hand pointing at 9 — exactly where it was before.

12 12
11 1 11 1
10 2 10 2
60 seconds later
9 3 9 3
8 4 8 4
7 5 7 5
6 6

Clock in the book Draw the red hand here

hour minute second

After one full round the seconds hand comes back to 9. The minute hand has moved on by one small
mark.

1. Left clock: the red hand is on 9, so the start reading is 45 seconds.
2. Add the time taken: 45 + 60 = 105 seconds.
3. Exchange 60 of them for 1 minute: 105 − 60 = 45. So it is 1 minute and 45 seconds later.
4. The whole minute is shown by the minute hand, not by the red hand. So the red hand ends
up back at 45 seconds, which is the number 9.

Page 26 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

45 s + 60 s = 105 s

105 s = 60 s + 45 s = 1 min 45 s

Seconds hand shows the leftover 45 s → the number 9

Why 60 seconds brings it back to the same place: One full round of the dial is 60
seconds. So after exactly 60 seconds the hand has come home. Take 120 seconds
and it would come home twice.

Also mark this: the green minute hand should now sit one small mark further on,
because a whole minute has passed.

Q4 (4) Ritu took 40 sec. to wash a plate.

Draw the seconds hand pointing at 7.

12 12
11 1 11 1
10 2 10 2
40 seconds later
9 3 9 3
8 4 8 4
7 5 7 5
6 6

Clock in the book Draw the red hand here

hour minute second

The seconds hand starts at 11 (55 seconds), sweeps past 12, and stops at 7 (35 seconds).

1. Left clock: the red hand is on 11. Count in fives: 5, 10, … , 55 seconds.
2. Add the time taken: 55 + 40 = 95 seconds.

Page 27 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

3. 95 is more than 60, so the hand has crossed the 12. Exchange 60 seconds for 1 minute: 95 −
60 = 35.
4. Find the number: 35 ÷ 5 = 7. Draw the thin hand to the 7.

55 s + 40 s = 95 s

95 s = 60 s + 35 s
60 s = 1 minute (carried to the minute hand)

Seconds hand shows 35 s → the number 7

Why we take away 60 and not 100: This is where time is different from ordinary
numbers. In ordinary counting we bundle up in tens. In time we bundle up in
sixties: 60 seconds make one minute, so as soon as we reach 60 we hand it over to
the minute hand and carry on from 0.

Count it on the dial instead: From 11 to 12 is 5 seconds. That leaves 40 − 5 = 35
seconds still to go from the top. 35 seconds from 12 is the number 7 ✓

Conversion of Hours to Minutes — Page 161

Page 28 of 48

as e
Class 5 Maths Chapter 12 Racing Seconds
a g l AglaSem · NCERT Solutions

Zainab and Remo, and the hours-and-minutes double number line
co m
e m.
com as
CONVERSION OF HOURS TO MINUTES LET US DO

. a g l
e m
g l as Use the double number line below to complete the conversions.
a
Q1 (a)

com
. ag
×2

e m
g l as
1 hr ___ hr a4 hr 7 hr __ hr 9 hr ___ hr ___ hr

co m
em.
m l as
.co g
60 min 120 min ___ min ___ min 480 min ___ min 660 min 720 min

m a
l a se
ag Page 161, Question 1 (a) — the double number line. Hours on the top line, minutes on
the bottom line.

m a s
m.co agl
l a se
a g
Here is the completed double number line. The answers are shown in red.

co m
m .
m as e
.co a g l
a s em 1 2 4 7 8 9 11 12

agl hours
se m
com g l a
. a
minutes
m
ase
60 120 240 420 480 540 660 720

agl
Every hour on the top line sits directly above its number of minutes on the bottom line.

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

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m .
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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

HOURS WORKING MINUTES

1 hr 1 × 60 60 min

2 hr 2 × 60 120 min

4 hr 4 × 60 240 min

7 hr 7 × 60 420 min

8 hr 8 × 60 480 min

9 hr 9 × 60 540 min

11 hr 11 × 60 660 min

12 hr 12 × 60 720 min

How to fill any blank on this line:

1. Blank on the bottom (minutes missing): take the hours above it and multiply by 60. For 4
hr → 4 × 60 = 240 min.
2. Blank on the top (hours missing): take the minutes below it and divide by 60. For 480 min
→ 480 ÷ 60 = 8 hr.

4 × 60 = 240 7 × 60 = 420 9 × 60 = 540

480 ÷ 60 = 8 660 ÷ 60 = 11 720 ÷ 60 = 12

120 ÷ 60 = 2

Why the line is drawn twice: The same moment of time can be named in two ways
— as hours or as minutes. Drawing them one above the other lets you slide from
one name to the other without any calculation at all. Just look straight up, or straight
down.

Check it yourself: 12 hours is half a day, and 720 minutes is what our line says. Test
it: 720 ÷ 60 = 12 ✓ Two of these make 1440 minutes, which is one whole day.

Page 30 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Q1 (b) (i) Do as instructed. You can use the double number line below.

×2

1 hr ___ hr 4 hr 7 hr __ hr 9 hr ___ hr ___ hr

60 min 120 min ___ min ___ min 480 min ___ min 660 min 720 min

Page 161 — the double number line from Question 1 (a). Hours on the top line,
minutes on the bottom line.

(i) 1 hours 10 minutes = _____ minutes

70 minutes.

1. Split it into two pieces: 1 hour, and 10 minutes.
2. Change the hour piece into minutes: 1 hour = 60 minutes.
3. Add the loose minutes: 60 + 10 = 70.

1 hour 10 minutes
= 60 min + 10 min

= 70 minutes

On the number line: find 1 hr on the top; below it is 60 min. Then step 10 more
minutes along the bottom line. You land on 70.

Q1 (b) (ii) (ii) 2 hours 45 minutes = _____ minutes

165 minutes.

1. Split: 2 hours, and 45 minutes.
2. Hours into minutes: 2 × 60 = 120 minutes.
3. Add: 120 + 45 = 165.

Page 31 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

2 hours 45 minutes

= (2 × 60) + 45

= 120 + 45
= 165 minutes

Check it yourself: 165 − 120 = 45, and 120 ÷ 60 = 2. So 165 minutes really is 2 hours
45 minutes ✓

Q1 (b) (iii) (iii) 3 hours 15 minutes = _____ minutes

195 minutes.

1. Split: 3 hours, and 15 minutes.
2. Hours into minutes: 3 × 60 = 180 minutes. (This is exactly what Remo says on page 161.)
3. Add: 180 + 15 = 195.

3 hours 15 minutes

= (3 × 60) + 15

= 180 + 15

= 195 minutes

Q1 (b) (iv) (iv) 4 hours 20 minutes = _____ minutes

260 minutes.

1. Split: 4 hours, and 20 minutes.
2. Hours into minutes: 4 × 60 = 240 minutes. You can read this straight off the double number
line.
3. Add: 240 + 20 = 260.

Page 32 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

4 hours 20 minutes

= (4 × 60) + 20

= 240 + 20

= 260 minutes

The pattern in (i) to (iv): hours × 60, then add the loose minutes. That one rule does
all four.

Q1 (b) (v) (v) 75 minutes = ____ hour ____ minutes

1 hour 15 minutes.
Now we go the other way, so we take out whole hours instead of putting them in.

1. Ask: how many whole 60s are hiding in 75? Just one, because 60 fits into 75 once and 120
would be too big.
2. Take out that hour: 75 − 60 = 15.
3. Name the two pieces: 1 hour, and 15 minutes left over.

75 ÷ 60 → 1 hour, remainder 15

75 minutes = 1 hour 15 minutes

Why we divide by 60 and not by 100: An hour is not made of a hundred minutes. It
is made of sixty. So when we bundle loose minutes into hours, we bundle them sixty
at a time.

Q1 (b) (vi) (vi) 150 minutes = ____ hours ____ minutes

2 hours 30 minutes.

1. How many whole 60s are in 150? 60 + 60 = 120, and one more 60 would make 180, which is
too big. So 2 hours.
2. Take them out: 150 − 120 = 30.

Page 33 of 48

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Class 5 Maths Chapter 12 Racing Seconds
a g l AglaSem · NCERT Solutions

3. So 150 minutes = 2 hours 30 minutes.
co m
e m.
m l as
m .co
150 ÷ 60 → 2 hours, remainder 30
a g
l a se
g
150 minutes = 2 hours 30 minutes
a

co m
.
Check it yourself: (2 × 60) + 30 = 120 + 30 = 150 ✓ Working backwards is the best
em ag
as
way to be sure.

a g l

co m
em.
(vii) 220 minutes = ____ hours ____ minutes

as
Q1 (b) (vii)

m l
.co a g
a s em
g3lhours 40 minutes.

a
m
1. Look at the number line. The nearest hour mark below 220 minutes is 180 minutes, which
a s
em
.co
is 3 hours. (240 minutes would be 4 hours — too big.)
agl
a s
gl
2. Take out those 3 hours: 220 − 180 = 40.
3. So 220 minutes = 3 hours 40aminutes.

co m
220 ÷ 60 → 3 hours, remainder 40
m .
m as e
.co
220 minutes = 3 hours 40 minutes
a g l
se m
g l a
a
m
Check it yourself: (3 × 60) + 40 = 180 + 40 = 220 ✓

a se
. com a g l
m
ase
Q1 (b) (viii) agl
(viii) 390 minutes = ____ hours ____ minutes

co m
m .
m as e
.co l
6 hours 30 minutes.
a g
s e m1. Count 60s up to 390: 60, 120, 180, 240, 300, 360. That is six 60s. The next one, 420, is bigger
agla than 390.

.c
m
2. So there are 6 whole hours inside 390 minutes.

m a s e
co agl
3. Take them out: 390 − 360 = 30.

m .
as
4. So 390 minutes = 6 hours 30 minutes.
e
a g l

co m
m .
m ase
.co


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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

390 ÷ 60 → 6 hours, remainder 30

390 minutes = 6 hours 30 minutes

Check it yourself: (6 × 60) + 30 = 360 + 30 = 390 ✓ That is a long school day — from
8 in the morning to half past two.

Let Us Do — Page 162
1 (c) Minutes and seconds on a double number line

LET US DO

Q1 (c) Fill in the blanks in the double number line to complete the conversions.

×5

1 min 5 min
___ min 10 min 15 min ___ min ___ min

× 60

120 sec ___ sec ___ sec 1200 sec 1500 sec
60 sec ___ sec

Page 162, Question 1 (c) — the double number line. Minutes on the top line, seconds
on the bottom line.

Here is the completed line. Every minute on top is worth 60 seconds below.

2
1 5 10 15 20 25
minutes

seconds
60 300 600 900 1200 1500
120

Page 35 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

The 2 minute mark is written a little away from the 1 minute mark so the labels do not touch.

MINUTES WORKING SECONDS

1 min 1 × 60 60 sec

2 min 2 × 60 120 sec

5 min 5 × 60 300 sec

10 min 10 × 60 600 sec

15 min 15 × 60 900 sec

20 min 1200 ÷ 60 1200 sec

25 min 1500 ÷ 60 1500 sec

5 × 60 = 300 10 × 60 = 600 15 × 60 = 900

1200 ÷ 60 = 20 1500 ÷ 60 = 25

The same rule twice: Hours become minutes by × 60, and minutes become seconds
by × 60 as well. Time is built in sixties all the way down. That is why the two double
number lines on pages 161 and 162 look so alike.

A quick way to multiply by 60: multiply by 6, then put a zero at the end. 15 × 6 = 90,
add a zero → 900. Try it on 25: 25 × 6 = 150, add a zero → 1500 ✓

Q1 (c) (i) (i) 320 sec = ____ min ____ sec

5 minutes 20 seconds.

1. Find the biggest whole minute inside 320 seconds. From the number line, 5 min = 300 sec.
The next mark, 6 min, would be 360 sec — too big.
2. Take out those 5 minutes: 320 − 300 = 20.
3. So 320 seconds = 5 minutes 20 seconds.

Page 36 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

320 ÷ 60 → 5 minutes, remainder 20

320 sec = 5 min 20 sec

Check it yourself: (5 × 60) + 20 = 300 + 20 = 320 ✓

Q1 (c) (ii) (ii) 225 sec = ____ min ____ sec

3 minutes 45 seconds.

1. Count 60s: 60, 120, 180. The next one is 240, which is more than 225. So 3 whole minutes.
2. Take them out: 225 − 180 = 45.
3. So 225 seconds = 3 minutes 45 seconds.

225 ÷ 60 → 3 minutes, remainder 45

225 sec = 3 min 45 sec

Check it yourself: 180 + 45 = 225 ✓ That is about how long one over of cricket takes.

Q1 (c) (iii) (iii) 700 sec = ____ min ____ sec

11 minutes 40 seconds.

1. Start from a mark you know. The number line says 10 min = 600 sec.
2. How much is left? 700 − 600 = 100 seconds.
3. 100 seconds is more than a minute, so take out one more minute: 100 − 60 = 40.
4. Add up the minutes taken out: 10 + 1 = 11 minutes, with 40 seconds left.

700 − 600 = 100 (10 minutes taken out)

100 − 60 = 40 (1 more minute taken out)

700 sec = 11 min 40 sec

Page 37 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Check it yourself: (11 × 60) + 40 = 660 + 40 = 700 ✓

Q1 (c) (iv) (iv) 1,000 sec = ____ min ____ sec

16 minutes 40 seconds.

1. Start from a mark you know. 15 min = 900 sec, from the number line.
2. How much is left? 1000 − 900 = 100 seconds.
3. Take out one more minute: 100 − 60 = 40.
4. Total minutes: 15 + 1 = 16, with 40 seconds left over.

1000 − 900 = 100 (15 minutes taken out)

100 − 60 = 40 (1 more minute taken out)

1000 sec = 16 min 40 sec

Why 1000 seconds is not 16 and a half minutes: Half of 60 is 30, not 40. The
leftover here is 40 seconds, which is two-thirds of a minute — a bit more than half.

Q1 (c) (v) (v) 10 min 13 sec = ____ sec

613 seconds.

1. Change the minutes into seconds: 10 × 60 = 600 seconds. The number line shows this
directly.
2. Add the loose seconds: 600 + 13 = 613.

10 min 13 sec

= (10 × 60) + 13

= 600 + 13

= 613 seconds

Page 38 of 48

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Class 5 Maths Chapter 12 Racing Seconds
a g l AglaSem · NCERT Solutions

co m
m.
(vi) 4 min 8 sec = ____ sec
e
Q1 (c) (vi)

m l as
.co a g
a
s em
a l
248gseconds.

1. Minutes into seconds: 4 × 60 = 240 seconds.

co m
2. Add the loose seconds: 240 + 8 = 248.
e m . ag
g l as
4 min 8 sec a
= (4 × 60) + 8
co m
em.
com as
= 240 + 8
. a g l
em
= 248 seconds
l a s
ag
Check it yourself: 248 − 240 = 8, and 240 ÷ 60 = 4 ✓
m a s
m .co agl
l a se
a g
(vii) 15 min 40 sec = ____ sec
Q1 (c) (vii)

co m
m .
m as e
.co a g l
em
940 seconds.

a s
gl
1. Minutes into seconds: 15 × 60 = 900 seconds. Read it off the number line, or do 15 × 6 = 90
a and add a zero.

se m
com a
2. Add the loose seconds: 900 + 40 = 940.

. a g l
m
ase
agl
15 min 40 sec

= (15 × 60) + 40

co m
= 900 + 40
m .
m as e
.co
= 940 seconds
a g l
se m
g l a
a c
Did you notice? In (iii) we found 700 sec = 11 min 40 sec, and here 15 min 40 sec =
m .
m
940 sec. The two questions are the same idea, just walked in opposite directions.
a s e
e m . co agl
g l as
a
Let Us Do (continued) — Page 162

co m
m .
m ase
.co


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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Adding up times, and finding how long a journey took

LET US DO

Q2 Raghav studies Mathematics, English, Hindi, and The World Around Us subjects. He
took 50 minutes to study each of the subjects. Find the total time taken in hours
and minutes. Share your strategies with your class.

Raghav studied for 3 hours 20 minutes in all.
What we must find: the total time for four subjects, when each subject took 50 minutes.

1. Count the subjects. Mathematics, English, Hindi, The World Around Us — that is 4 subjects.
2. Find the total in minutes. Four lots of 50 minutes: 50 × 4 = 200 minutes.
3. Change 200 minutes into hours. Count 60s: 60, 120, 180. The next one, 240, is too big. So
there are 3 whole hours.
4. Find the leftover: 200 − 180 = 20 minutes.
5. Write the answer with both units: 3 hours 20 minutes.

Time for one subject = 50 minutes

Number of subjects = 4

Total = 50 × 4 = 200 minutes

200 = 180 + 20 = (3 × 60) + 20

Total time = 3 hours 20 minutes

Sample answer for ‘share your strategies’: I did not multiply at first. I added in pairs, because
50 + 50 is easy. 50 + 50 = 100 minutes for two subjects. Another 50 + 50 = 100 minutes for the
other two. 100 + 100 = 200 minutes altogether. Then I took out hours 60 at a time until only 20
minutes were left.

Another neat strategy: 50 minutes is 10 minutes short of an hour. Four subjects
would be 4 hours if each took a full hour. But each is short by 10 minutes, so
altogether we are short by 4 × 10 = 40 minutes. 4 hours − 40 minutes = 3 hours 20
minutes. Same answer, and no big multiplication at all.

Check it yourself: 3 hours 20 minutes = 180 + 20 = 200 minutes, and 200 ÷ 50 = 4
subjects ✓

Page 40 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Q3 Raghu left his house at 08:00 hours and arrived at his Nana ji’s house at 09:05 hours.
How long did he take to reach his house?

Raghu took 1 hour 5 minutes.
The book shows the neat way to do this — jump forward in easy hops instead of writing a
subtraction sum.

1. Hop 1 — to the next full hour. 08:00 hours to 09:00 hours is 1 hour.
2. Hop 2 — the leftover minutes. 09:00 hours to 09:05 hours is 5 minutes.
3. Add the hops. 1 hour + 5 minutes = 1 hour 5 minutes.

08:00 → 09:00 = 1 hour

09:00 → 09:05 = 5 minutes

Time taken = 1 hour 5 minutes

Why not just do 09:05 − 08:00 in columns? Here it happens to work, because 5
minutes is more than 0 minutes. But if he had arrived at 08:55 and left at 08:00 you
would be fine, while a start of 08:40 and an arrival of 09:05 would need borrowing —
and time borrows 60, not 10. Hopping forward never runs into that trouble.

In minutes: 1 hour 5 minutes = 60 + 5 = 65 minutes. Note also that these are 24-
hour format times, so 08:00 hours means 8 o'clock in the morning.

Let Us Do — Page 163
Start time, end time and duration word problems

LET US DO

Q4 Jyoti went to play at 06:15 PM. She came back after 1 hour 45 minutes. At what time
did she reach home?

Jyoti reached home at 08:00 PM.
What we must find: the finishing time, when we know the starting time and how long she
played.

Page 41 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

1. Add the whole hours first. 06:15 PM + 1 hour = 07:15 PM.
2. Now add the minutes. 15 minutes + 45 minutes = 60 minutes.
3. 60 minutes is a whole hour, so it is not written as 07:60. Exchange it: 60 minutes = 1 hour, 0
minutes.
4. Carry that hour: 07 + 1 = 08, and the minutes become 00.
5. So she reached home at 08:00 PM.

06 hr : 15 min

+ 01 hr : 45 min

─────────────

07 hr : 60 min

60 min = 1 hour, so carry 1

= 08:00 PM

Why we cannot write 07:60: A clock never shows 60 minutes. As soon as the
minutes reach 60, they turn into one more hour and the minute count starts again at
0. This is the base-sixty carry, and it is the only thing that makes time sums different
from ordinary addition.

Check it yourself: Go backwards from 08:00 PM. Take away 1 hour → 07:00 PM.
Take away 45 minutes → 06:15 PM ✓ That is where she started.

Q5 Ragini took 1 hour 10 minutes to do her homework. She finished it at 09:40 PM.
What time did she start?

Ragini started at 08:30 PM.
This time we know the end, so we must walk backwards.

1. Go back the whole hour first. 09:40 PM − 1 hour = 08:40 PM.
2. Now go back the minutes. 40 minutes − 10 minutes = 30 minutes.
3. So the starting time was 08:30 PM.

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

09 hr : 40 min (finished)

− 01 hr : 10 min (time taken)

─────────────

08 hr : 30 min → 08:30 PM

No borrowing was needed here because 40 minutes is bigger than 10 minutes. If
she had finished at 09:05 PM instead, we could not take 10 from 5. Then we would
borrow 1 hour and turn it into 60 minutes: 5 becomes 65, and 65 − 10 = 55, giving
08:55 PM.

Check it yourself: 08:30 PM + 1 hour = 09:30 PM, and + 10 minutes = 09:40 PM ✓

Q6 A group of children left for a picnic at 08:30 AM. They returned after 4 hours and 10
minutes. At what time did they return?

They returned at 12:40 PM.

1. Add the hours. 08:30 AM + 4 hours: 8 → 9 → 10 → 11 → 12. So we reach 12:30.
2. Watch out for noon. Once we pass 12 o'clock in the middle of the day, the label changes
from AM to PM. 12:30 in the middle of the day is 12:30 PM.
3. Add the minutes. 30 + 10 = 40 minutes. This is less than 60, so nothing is carried.
4. They returned at 12:40 PM.

08:30 AM + 4 hours = 12:30 PM

12:30 PM + 10 minutes = 12:40 PM

Why the AM turned into PM: AM covers midnight to noon, PM covers noon to
midnight. The picnic started in the morning and finished after 12 noon, so it crossed
the changeover point.

In 24-hour format this is much simpler: 08:30 hours + 4:10 = 12:40 hours, with no
AM or PM to worry about at all. That is exactly why timetables use it.

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as e
Class 5 Maths Chapter 12 Racing Seconds
a g l AglaSem · NCERT Solutions

co m
m.
Raji started her homework at 06:00 PM. She finished her homework in 1 hour 30
e
Q7

m l as
.co
minutes. At what time did she finish?

a g
se m
g l a
a

Raji finished at 07:30 PM.

1. Add the hour. 06:00 PM + 1 hour = 07:00 PM.
. c om ag
2. Add the minutes. 07:00 PM + 30 minutes
s e m= 07:30 PM.
3. Since 0 + 30 = 30, which is less thanla
ag
60, there is nothing to carry.

co m
m.
06 hr : 00 min

m as e
.co l
+ 01 hr : 30 min
a g
se m
a
─────────────

a g l 07 hr : 30 min → 07:30 PM

om a s
On the clock face: the hour hand m
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. c agl
s
slides from 6 to halfway between 7 and 8, and the
a
agl and then half way, stopping at the 6. Half past seven.
minute hand goes once round

co m
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as e
om does she come back? l
Alya goes out to play at 05:30 PM and comes back after 1 hour 10 minutes. At what
.ctime g
Q8

m a
l a se
ag ANSWER

se m
com l a
Alya comes back at 06:40 PM.
. a g
s e m
1. Add the hour. 05:30 PM + 1 hour = 06:30 PM.
2. Add the minutes. 30 + 10 =la
a g 40 minutes.
3. 40 is less than 60, so the hour does not change again. She is back at 06:40 PM.

co m
m .
05 hr : 30 min
m as e
.+co01 hr : 10 min a g l
se m
g l a
a
─────────────
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06 hr : 40 min → 06:40 PM
s e m
m a
e m . co agl
g l as
a

co m
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m ase
.co


a g l Page 44 of 48

Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Check it yourself: 1 hour 10 minutes = 70 minutes. From 05:30 PM, 30 minutes
takes her to 06:00 PM, and the remaining 40 minutes takes her to 06:40 PM ✓

Q9 If the lunch break of a school starts at 12:30 PM and ends in 35 minutes, what time
will lunch end?

Lunch will end at 01:05 PM.

1. Add the minutes. 30 + 35 = 65 minutes.
2. 65 is more than 60, so we must exchange. 65 = 60 + 5.
3. The 60 becomes one whole hour and is carried to the hour column. Only 5 minutes stay
behind.
4. Add the carried hour. 12 o'clock + 1 hour = 1 o'clock.
5. So lunch ends at 01:05 PM.

12 hr : 30 min

+ 00 hr : 35 min

─────────────

12 hr : 65 min

65 min = 60 min + 5 min = 1 hr 5 min
12 hr + 1 hr = 13 hr → 01:05 PM

Why 12 turns into 1 and not 13: On the 12-hour clock the numbers go up to 12 and
then start again at 1. So the hour after 12 noon is 1 PM. In the 24-hour format,
though, we really do write 13:05 hours.

Check it yourself: From 12:30 PM, 30 minutes takes you to 01:00 PM. Then 5 more
minutes makes 01:05 PM. And 30 + 5 = 35 minutes ✓

Q10 It is 08:35 PM right now. What time will it be after 8 hours and 25 minutes?

It will be 05:00 AM the next morning.

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

1. Add the hours first. 08:35 PM + 8 hours. Count on: 9, 10, 11, 12 (that is 4 hours and we are
at midnight), then 1, 2, 3, 4 (four more hours). We reach 04:35 AM.
2. Notice the date has changed. We crossed 12 midnight, so PM became AM and it is now the
next morning.
3. Now add the minutes. 35 + 25 = 60 minutes.
4. 60 minutes is one whole hour, so exchange it: the minutes become 00 and one more hour
is carried.
5. Add that hour: 04 + 1 = 05. So the time is 05:00 AM.

08:35 PM + 8 hours = 04:35 AM (next day)

35 min + 25 min = 60 min = 1 hour

04:35 AM + 25 min = 05:00 AM

Why midnight matters: Midnight is where one day ends and the next begins.
Adding 8 hours to 8:35 in the night carries us right past it, so the answer is a time on
the following day — early morning, when the sun is not yet up.

Easier in 24-hour format: 08:35 PM is 20:35 hours. 20:35 + 8:25 = 28:60 hours. Now
tidy it up: 60 minutes = 1 hour, so 29:00 hours. And 29 − 24 = 5, so it is 05:00 hours
the next day ✓ Same answer.

Chapter at a glance
A second is a very small piece of time. Say one thousand one out loud — that takes about
one second. Blinking your eyes takes less than a second. The thin red hand on a wall clock is
the seconds hand. It is the fastest hand: it goes right round the dial in one minute.
60 seconds make 1 minute. 60 minutes make 1 hour. This is the one fact the whole
chapter rests on. Watch the seconds hand: after it has ticked 60 little marks it has gone once
round, and the minute hand has moved on by exactly one mark. So 1 min = 60 s and 1 hr =
60 min.
Time is counted in sixties, not in tens. In money, 10 tens make 100. In time, it is 60 that
makes the next unit. So when seconds add up past 60, we carry 1 to the minutes. 40 s + 35 s
= 75 s = 1 min 15 s. And when we cannot subtract, we borrow 1 minute and it becomes 60
seconds, not 10.
Reading a clock with three hands. Look at the short thick hand first — that is the hour
hand; the number it has just passed is the hour. Then the long hand — the minute hand;
count the small marks from 12 in fives. Then the thin hand — the seconds hand; count the

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

small marks from 12 in fives again. A clock showing hour hand between 5 and 6, minute
hand on 7 and seconds hand on 12 reads 5:35 and 0 seconds.
The 12-hour way and the 24-hour way. A day has 24 hours, but a clock face has only 12
numbers. So the same 12 numbers are used twice — once for a.m. (midnight to noon) and
once for p.m. (noon to midnight). Railways and airports do not use a.m. and p.m. at all. They
count straight on from 00 to 23. Rule: an a.m. time stays the same; for a p.m. time add 12 to
the hour. So 05:30 p.m. = 05:30 + 12:00 = 17:30 hours.
Changing hours into minutes: multiply by 60. 3 hours = 3 × 60 = 180 minutes. To change
minutes back into hours, divide by 60: 180 ÷ 60 = 3 hours. A leftover is written as minutes:
220 ÷ 60 gives 3 with 40 left over, so 220 min = 3 hours 40 minutes.
Changing minutes into seconds: multiply by 60 again. 5 min = 5 × 60 = 300 seconds. And
back the other way, divide by 60: 320 ÷ 60 gives 5 with 20 left over, so 320 s = 5 min 20 s.
Finding how long something took. Do not start with a subtraction sum. Start at the earlier
time and jump forward in easy hops — first whole hours, then the extra minutes. From
08:00 to 09:00 is one hop of 1 hour; from 09:00 to 09:05 is another hop of 5 minutes. Total 1
hour 5 minutes. Adding a duration works the same way, only forwards.
Which unit — seconds or minutes? Ask yourself: could I count it while holding my breath?
Snapping your fingers, blinking, sitting down — seconds. Melting an ice cube, making a
phone call — minutes. Choosing the right unit is part of measuring well.

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Class 5 Maths Chapter 12 Racing Seconds AglaSem · NCERT Solutions

Quick revision

WORD WHAT IT MEANS WHERE IT APPEARS EXAMPLE

Second The smallest unit of time in this Page 157, the race Snapping your fingers
chapter; 60 of them make one minute stopwatches takes about 1 second

Minute 60 seconds Page 157, 1 min = 60 The winner took 1 minute
seconds 55 seconds

Hour 60 minutes Page 161, Conversion of Rani painted for 2 hours
Hours to Minutes 10 minutes

Seconds hand The thin, fastest hand of a clock; one Pages 159 and 160 Red hand pointing at 6
full round = 1 minute means 30 seconds

Minute hand The long hand; it moves one small Pages 155, 159, 160 Green hand on 9 means
mark when the seconds hand goes 45 minutes
once round

Hour hand The short, thick hand; it tells the hour Pages 155, 159, 160 Blue hand between 5 and
6 means the hour is 5

a.m. The 12 hours from midnight to noon Page 156, the time- 05:30 a.m. is early
format table morning

p.m. The 12 hours from noon to midnight Page 156, the time- 09:35 p.m. is night
format table

12-hour format Time written with a.m. or p.m. Page 156, left column 02:30 p.m.

24-hour format Time counted straight on from 00 to Page 156, right column 02:30 p.m. = 14:30 hours
23 hours, with no a.m. or p.m.

Time elapsed How much time passed between a Page 155, question 4 09:15 a.m. to 11:30 a.m.
(duration) start time and an end time is 2 hours 15 minutes

Double Two number lines drawn one above Pages 161 and 162 1 hr above, 60 min below
number line the other so matching values line up

Estimate A sensible guess made before Page 157, Let Us Do Guess how many hops in
measuring a minute, then count

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