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CBSE · Class 5 · Math Mela

Chapter 12: Racing Seconds (Time)

6 concepts · 48 practice questions with answers · Free to read

This lesson is also in: मराठी · हिंदी

Reading time: a.m., p.m. and the 24-hour clock

From daily life

The school bell rings at 8:00 in the morning and the evening prayer is at 8:00 at night. Both say "8 o'clock"! We add a.m. or p.m., or use the 24-hour clock, so nobody gets confused.

Simple definition

A day has 24 hours. a.m. is from midnight to noon; p.m. is from noon to midnight. The 24-hour clock counts 00:00 to 23:59 and needs no a.m. or p.m. The short hand shows hours, the long hand shows minutes.

Formula: p.m. (after 1 o'clock): 24-hour = 12-hour + 12. a.m.: the hour stays the same. 12 noon = 12:00, 12 midnight = 00:00.

1234567891011121234567891011124:309:15

12 a.m.12 noon12 a.m.a.m.p.m.00:0006:0012:0015:0024:000 – 1112 – 233 p.m. = 12 + 3 = 15:00

In the figure: Left clock: hour hand between 4 and 5, minute hand at 6: 4:30. Right clock: 9:15. The line shows a.m. (0–11) and p.m. (12–23); 3 p.m. is 15:00.

Rule 1: 12-hour to 24-hour — For p.m. add 12 to the hour (except 12 p.m.). For a.m. keep the hour; 12:30 a.m. becomes 00:30.

  • Easy: 07:45 p.m. = 19:45.
  • Medium: 09:10 a.m. = 09:10.
  • Exam-type: 12:30 a.m. = 00:30; 12:30 p.m. = 12:30.

Rule 2: 24-hour to 12-hour — If the hour is more than 12, subtract 12 and write p.m. If it is less than 12, write a.m.

Live figure

Reading time: a.m., p.m. and the 24-hour clock

In the app you can move this figure with your finger.

Open in the app
  • Easy: 18:20 = 06:20 p.m.
  • Medium: 05:55 = 05:55 a.m.
  • Exam-type: 23:40 = 11:40 p.m.
Remember

The hour hand moves slowly; the minute hand moves 12 times as fast. Each number on the clock face is 5 minutes.

Common mistake

Writing 15:00 as 3 a.m., or adding 12 to an a.m. time.

Shortcut

Minute hand at 3 = 15 min, 6 = 30 min, 9 = 45 min. Memory clue: "After noon add twelve."

Spot the difference

12-hour24-hour
12:00 a.m.00:00
06:30 a.m.06:30
12:00 p.m.12:00
03:15 p.m.15:15
11:59 p.m.23:59

Practice questions

Easy
  1. 1Write 05:20 p.m. in the 24-hour format.
  2. 2Write 08:05 a.m. in the 24-hour format.
  3. 3Write 21:45 in the 12-hour format.
Medium
  1. 4Write 00:15 in the 12-hour format.
  2. 5The hour hand is just past 7 and the minute hand points at 3. What is the time?
  3. 6Which is later: 10:30 p.m. or 21:50?
Challenging
  1. 7A train leaves at 14:35. Write this in a.m./p.m. and say how many minutes after 2 o'clock it leaves.
  2. 8Put in order, earliest first: 18:10, 04:45 p.m., 09:00 a.m., 23:05.
Show answers (try them yourself first)
  1. 117:20
  2. 208:05
  3. 309:45 p.m.
  4. 412:15 a.m.
  5. 57:15
  6. 610:30 p.m. (22:30)
  7. 702:35 p.m.; 35 minutes
  8. 809:00 a.m., 04:45 p.m. (16:45), 18:10, 23:05

Seconds, minutes and estimating time

From daily life

A sprinter finishes a 100 m race in a few seconds, but cooking rice takes minutes. For tiny moments we need a tiny unit: the second.

Simple definition

1 minute = 60 seconds. The thin red hand of a clock is the seconds hand; it goes once round in 1 minute. Each number on the clock is 5 seconds. Use seconds for short events and minutes for longer ones.

Formula: 1 min = 60 s. Seconds hand at number n: n × 5 seconds. Lower time = faster.

1234567891011120 s15 s1 min= 60 s1 number= 5 s

In the figure: The seconds hand at 3 has moved 3 × 5 = 15 seconds. A full round is 60 seconds = 1 minute.

Rule 1: Choose seconds or minutes — Blinking, a clap, a sprint: seconds. Boiling water, a cartoon, a bus ride: minutes.

Live figure

Seconds, minutes and estimating time

In the app you can move this figure with your finger.

Open in the app
  • Easy: Washing hands: about 20 seconds.
  • Medium: Filling a bucket: about 2 minutes.
  • Exam-type: Counting 1 to 20: about 15 seconds.

Rule 2: Compare race times — Change everything to seconds, then compare. The smallest time wins.

  • Easy: 2 min 8 s = 128 s; 2 min 5 s = 125 s: the 125 s runner wins.
  • Medium: Gap between 125 s and 131 s: 6 seconds.
  • Exam-type: 14 s + 17 s = 31 s together.
Remember

1 hour = 60 min and 1 min = 60 s, so 1 hour = 3,600 seconds.

Common mistake

Thinking 1 minute has 100 seconds, or reading the seconds hand number as seconds without multiplying by 5.

Shortcut

Count in 5s round the clock: 5, 10, 15 … Memory clue: "Sixty seconds, one minute."

Spot the difference

UnitEquals
1 minute60 seconds
1 hour60 minutes
1 hour3,600 seconds
1 day24 hours

Practice questions

Easy
  1. 14 minutes = ? seconds
  2. 2The seconds hand points at 9. How many seconds?
  3. 3Seconds or minutes for brushing your teeth?
Medium
  1. 4Racers took 1 min 52 s, 1 min 48 s and 1 min 55 s. Who won?
  2. 5How many seconds in 2 minutes 30 seconds?
  3. 6A girl skips 2 times each second. How many skips in 1 minute?
Challenging
  1. 7A song lasts 3 min 20 s. How many seconds is that?
  2. 8Racer A needs 45 s per lap, racer B needs 50 s per lap. After 6 laps, how many seconds ahead is A?
Show answers (try them yourself first)
  1. 1240
  2. 245
  3. 3Minutes (about 2)
  4. 41 min 48 s
  5. 5150
  6. 6120
  7. 7200
  8. 86 × 5 = 30 seconds

Converting hours, minutes and seconds

From daily life

A film is 150 minutes long. Is that more or less than 2 hours? To compare we turn both into the same unit.

Simple definition

To go from a bigger unit to a smaller one (hours to minutes, minutes to seconds) multiply by 60. To go from smaller to bigger divide by 60; the remainder is the smaller unit left over.

Formula: h → min: × 60. min → s: × 60. min → h: ÷ 60 (quotient = hours, remainder = minutes). s → min: ÷ 60.

0016021203180hmin× 603 h = 180 min

In the figure: Double number line: 0, 1, 2, 3 hours sit above 0, 60, 120, 180 minutes. Each hour adds 60 minutes.

Rule 1: Big to small: multiply — Multiply the hours by 60 and add the extra minutes.

Live figure

Converting hours, minutes and seconds

In the app you can move this figure with your finger.

Open in the app
  • Easy: 3 h = 3 × 60 = 180 min.
  • Medium: 2 h 25 min = 120 + 25 = 145 min.
  • Exam-type: 7 min 21 s = 420 + 21 = 441 s.

Rule 2: Small to big: divide — Divide by 60. The quotient is the big unit and the remainder is the small unit.

  • Easy: 95 min: 95 ÷ 60 = 1 remainder 35, so 1 h 35 min.
  • Medium: 205 min = 3 h 25 min.
  • Exam-type: 380 s = 6 min 20 s.
Remember

A remainder can never be 60 or more, because then another whole unit fits.

Common mistake

Multiplying by 100 instead of 60, or writing 1 h 75 min.

Shortcut

Think of 60 as "one more hour" in minutes: 60, 120, 180 … Memory clue: "Down the ladder multiply, up the ladder divide."

Spot the difference

ChangeDo this
h → min× 60
min → s× 60
min → h÷ 60
s → min÷ 60

Practice questions

Easy
  1. 15 hours = ? minutes
  2. 23 hours 20 minutes = ? minutes
  3. 3240 minutes = ? hours
Medium
  1. 4130 minutes = ? hours ? minutes
  2. 55 min 40 s = ? seconds
  3. 6500 seconds = ? min ? s
Challenging
  1. 7Which is longer: 2 hours or 100 minutes? By how many minutes?
  2. 8A film is 2 h 40 min long and a cartoon is 95 min long. How many minutes longer is the film?
Show answers (try them yourself first)
  1. 1300
  2. 2200
  3. 34 hours
  4. 42 h 10 min
  5. 5340
  6. 68 min 20 s
  7. 72 hours, by 20 minutes
  8. 8160 − 95 = 65 minutes

Time elapsed between two times

From daily life

Raghu's bus leaves at 9:10 a.m. and reaches at 11:55 a.m. How long was the journey? We find the time that passes between the two clock times.

Simple definition

Elapsed time is the time that passes from a start time to an end time. Count in jumps: first to the next whole hour, then whole hours, then the last minutes. Then add the jumps.

Formula: Elapsed time = end time − start time. Jump method: to the next hour + whole hours + extra minutes.

9:1010:0011:5550 min1 h 55 min9:10 → 10:00 → 11:5550 min + 1 h 55 min? Use jumps to the hour!

In the figure: 9:10 to 10:00 is 50 minutes; 10:00 to 11:55 is 1 hour 55 minutes. Together 2 hours 45 minutes.

Rule 1: Same side of noon — Subtract hours and minutes. If the end minutes are smaller, borrow 1 hour = 60 minutes.

Live figure

Time elapsed between two times

In the app you can move this figure with your finger.

Open in the app
  • Easy: 10:20 to 11:05: 45 minutes.
  • Medium: 13:10 to 16:40: 3 h 30 min.
  • Exam-type: 09:10 a.m. to 11:55 a.m.: 2 h 45 min.

Rule 2: Across noon or midnight — Change both times to the 24-hour clock first. Across midnight add 24 hours to the end time.

  • Easy: 11:20 a.m. to 02:05 p.m. = 11:20 to 14:05: 2 h 45 min.
  • Medium: 23:20 to 05:50 next day: 6 h 30 min.
  • Exam-type: 06:15 p.m. to 09:00 p.m.: 18:15 to 21:00 = 2 h 45 min.
Remember

Draw a time line with jumps; it works every time.

Common mistake

Subtracting minutes the wrong way round (35 − 50) instead of borrowing 60.

Shortcut

Jump to the next hour first, then add. Memory clue: "Hop to the hour, then hop on."

Spot the difference

FromToTime passed
10:2011:0545 min
13:1016:403 h 30 min
23:2005:506 h 30 min

Practice questions

Easy
  1. 1From 8:15 a.m. to 9:00 a.m. how long?
  2. 2From 2:30 p.m. to 5:10 p.m. how long?
  3. 3A film runs from 06:45 p.m. to 09:20 p.m. How long?
Medium
  1. 4A bus leaves at 10:40 a.m. and arrives at 01:15 p.m. Journey time?
  2. 5A night train leaves at 22:30 and reaches at 04:10. Journey time?
  3. 6Mohan studies from 5:20 p.m. to 6:05 p.m. and again from 7:00 p.m. to 8:10 p.m. Total study time?
Challenging
  1. 7Which journey is longer: 09:50 to 12:20, or 14:10 to 16:45?
  2. 8A shop is open from 08:30 a.m. to 01:00 p.m. and again from 04:00 p.m. to 08:15 p.m. How long is it open in a day?
Show answers (try them yourself first)
  1. 145 minutes
  2. 22 h 40 min
  3. 32 h 35 min
  4. 42 h 35 min
  5. 55 h 40 min
  6. 645 + 70 = 115 min = 1 h 55 min
  7. 7The second: 2 h 35 min vs 2 h 30 min
  8. 84 h 30 min + 4 h 15 min = 8 h 45 min

Finding the end or the start time

From daily life

The match starts at 6:15 a.m. and lasts 1 hour 50 minutes. When will it end? Or: the lesson ended at 2:10 p.m. after 50 minutes; when did it begin?

Simple definition

If you know the start and the duration, add to get the end time. If you know the end and the duration, subtract to get the start time. If minutes go past 60 make one more hour.

Formula: End = start + duration. Start = end − duration. Duration = end − start.

123456789101112123456789101112+ 1 h 50 min6:158:05

In the figure: 6:15 + 1 hour 50 minutes: 7:15, then 50 more minutes makes 8:05.

Rule 1: Add to find the end — Add the hours first, then the minutes. If minutes reach 60 or more, carry 1 hour.

Live figure

Finding the end or the start time

In the app you can move this figure with your finger.

Open in the app
  • Easy: 06:15 a.m. + 1 h 50 min = 08:05 a.m.
  • Medium: 04:40 p.m. + 2 h 35 min = 07:15 p.m.
  • Exam-type: 11:30 p.m. + 1 h 45 min = 01:15 a.m. next day.

Rule 2: Subtract to find the start — Go back by the duration. If the minutes are not enough, borrow 1 hour = 60 minutes.

  • Easy: 02:10 p.m. − 50 min = 01:20 p.m.
  • Medium: 09:05 p.m. − 1 h 25 min = 07:40 p.m.
  • Exam-type: 00:20 − 45 min = 23:35 the day before.
Remember

Check by going the other way: if end − start gives the same duration you are right.

Common mistake

Forgetting to carry 1 hour when minutes pass 60, or mixing a.m. and p.m.

Shortcut

Add whole hours first, minutes after. Memory clue: "Forward add, backward subtract."

Spot the difference

KnowFindDo
Start + durationEndadd
End + durationStartsubtract
Start + endDurationsubtract

Practice questions

Easy
  1. 1Start 7:20 a.m., lasts 40 minutes. End?
  2. 2Start 3:45 p.m., lasts 1 h 30 min. End?
  3. 3End 6:10 p.m., lasted 2 h 20 min. Start?
Medium
  1. 4End 10:05 a.m., lasted 55 minutes. Start?
  2. 5A film starts at 17:50 and lasts 2 h 25 min. End in the 24-hour format?
  3. 6A bus reaches at 00:25 after a journey of 3 h 40 min. When did it leave (24-hour)?
Challenging
  1. 7Lunch starts at 12:35 p.m. and lasts 40 minutes; class then lasts 1 h 10 min. When does class end?
  2. 8A film ends at 09:05 p.m. It ran 2 h 45 min including a 15-minute interval. When did it start?
Show answers (try them yourself first)
  1. 108:00 a.m.
  2. 205:15 p.m.
  3. 303:50 p.m.
  4. 409:10 a.m.
  5. 520:15
  6. 620:45
  7. 701:15 p.m., then 02:25 p.m.
  8. 806:20 p.m. (interval already counted)

Time word problems

From daily life

A school day, a train timetable, a race on sports day: real life is full of questions with time. Read, find what is asked, choose add, subtract, multiply or divide.

Simple definition

Steps: (1) write the times in one style (24-hour is easiest); (2) change hours to minutes if needed; (3) calculate; (4) change back to hours and minutes; (5) check that the answer makes sense.

Formula: Total time for equal parts = number × time of one part. Time of one part = total ÷ number.

4 subjects × 50 min4 × 50 = 200 min606060 + 20200 min = 3 h 20 min

In the figure: 4 × 50 = 200 minutes. 200 = 60 + 60 + 60 + 20, so 3 hours 20 minutes.

Rule 1: Equal parts — Many equal jobs: multiply. Share a total equally: divide. Then change the answer to hours or minutes.

Live figure

Time word problems

In the app you can move this figure with your finger.

Open in the app
  • Easy: 5 laps of 58 s: 5 × 58 = 290 s = 4 min 50 s.
  • Medium: 3 skips each second for 40 s: 3 × 40 = 120 skips.
  • Exam-type: 180 minutes shared by 4 friends: 45 minutes each.

Rule 2: Many steps — Do one step at a time and write the new time after each step.

  • Easy: Lunch at 12:30 p.m. for 35 min → 01:05 p.m.; class 1 h 40 min → 02:45 p.m.
  • Medium: Bus 09:20 a.m. to 12:05 p.m. = 09:20 to 12:05 = 2 h 45 min.
  • Exam-type: Two races 14 s and 17 s: together 31 s; difference 3 s.
Remember

1 day = 24 hours = 1,440 minutes. Keep this in mind for big problems.

Common mistake

Mixing hours and minutes in one subtraction, or forgetting that an interval inside a film is already counted.

Shortcut

Underline the times and units in the question first. Memory clue: "Same unit, then calculate."

Spot the difference

Question saysDo
each / everymultiply
shared equallydivide
how much longersubtract
altogetheradd

Practice questions

Easy
  1. 1A lesson lasts 45 minutes. How long are 6 lessons, in hours and minutes?
  2. 2A runner takes 62 seconds a lap. Time for 4 laps?
  3. 3A film starts at 4:15 p.m. and runs 2 h 30 min. When does it end?
Medium
  1. 4How many minutes are there in 2 days?
  2. 5Neha reads for 35 minutes each day for a week. Total time?
  3. 6A 3-hour programme has 5 equal shows with no breaks. How long is each show?
Challenging
  1. 7School starts at 8:20 a.m. and ends at 2:35 p.m. with a 45-minute break. How long are the classes in all?
  2. 8Two friends run 400 m. Asha takes 1 min 18 s, Bela takes 85 s. Who is faster and by how many seconds?
Show answers (try them yourself first)
  1. 1270 min = 4 h 30 min
  2. 2248 s = 4 min 8 s
  3. 306:45 p.m.
  4. 42,880
  5. 5245 min = 4 h 5 min
  6. 6180 ÷ 5 = 36 minutes
  7. 76 h 15 min − 45 min = 5 h 30 min
  8. 8Asha (78 s), by 7 seconds