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State Board · Class 5 · Mathematics

Lesson 10: Measuring Time

5 concepts · 40 practice questions with answers · Free to read

This lesson is also in: मराठी

Units of time and conversion

From daily life

A school period is 40 minutes and a school day has 6 periods. To know how many hours you study, you change minutes into hours. We use units of time every day.

Simple definition

Time is measured in seconds, minutes, hours, days, weeks, months and years. 1 min = 60 s, 1 hour = 60 min, 1 day = 24 hours, 1 week = 7 days, 1 year = 12 months.

Units of time: 1 minute = 60 seconds, 1 hour = 60 minutes, 1 day = 24 hours, 1 week = 7 days, 1 year = 12 months.1 minute=60 seconds1 hour=60 minutes1 day=24 hours1 week=7 days1 year=12 months

In the figure : Units of time and how they are linked.

Rule 1: Bigger to smaller unit: multiply — Multiply by the number of small units in one big unit.

  • Easy : 4 hours = 4 × 60 = 240 minutes.
  • Medium : 3 days = 3 × 24 = 72 hours.
  • Exam-type : 1 week = 7 × 24 = 168 hours.

Rule 2: Smaller to bigger unit: divide — Divide by the number of small units in one big unit; the remainder is the smaller unit.

  • Easy : 150 seconds = 2 min 30 s (150 ÷ 60 = 2, remainder 30).
  • Medium : 200 minutes = 3 hours 20 minutes.
  • Exam-type : 100 hours = 4 days 4 hours (100 ÷ 24 = 4, remainder 4).
Remember

Mixed time: change the bigger part and add. 1 hour 20 minutes = 60 + 20 = 80 minutes.

Common mistake

Dividing when you should multiply. Going from hours to minutes the number gets bigger.

Shortcut

Memory clue: Big to small × ; small to big ÷.

Spot the difference

UnitEqual to
1 minute60 seconds
1 hour60 minutes
1 day24 hours

Practice questions

Easy
  1. 1Change 5 minutes to seconds.
  2. 2Change 3 days to hours.
  3. 3Change 2 years to months.
Medium
  1. 4Change 200 minutes to hours and minutes.
  2. 5Change 1 hour 20 minutes to minutes.
  3. 6Change 3 weeks 2 days to days.
Challenging
  1. 7Mira studies 6 periods of 40 minutes. How many hours is that?
  2. 8Change 100 hours to days and hours. Then check by multiplying.
Show answers (try them yourself first)
  1. 1300 seconds
  2. 272 hours
  3. 324 months
  4. 43 hours 20 minutes
  5. 580 minutes
  6. 623 days
  7. 76 × 40 = 240 min = 4 hours
  8. 84 days 4 hours. Check: 4 × 24 + 4 = 100.

Reading the clock and 24-hour time

From daily life

The school bell rings at 7:30 in the morning, and a train leaves at 18:45 on the railway board. The clock and the 24-hour time tell the same time in two ways.

Simple definition

The short hand shows hours and the long hand shows minutes. a.m. is midnight to noon; p.m. is noon to midnight. The 24-hour clock runs from 00:00 to 23:59.

A clock showing 4:20: the short hand near 4 and the long hand on 4, which is 20 minutes.123456789101112short hand → hourslong hand → minuteseach number = 5 min4 : 20

In the figure : A clock at 4:20: the short hand shows the hours, the long hand shows the minutes.

Rule 1: Reading the minutes — Each number on the dial is 5 minutes.

  • Easy : Long hand on 3 = 15 min (quarter past); on 6 = 30 min; on 9 = 45 min (quarter to).
  • Medium : Long hand on 8 = 8 × 5 = 40 minutes.
  • Exam-type : Short hand just past 4 and long hand on 4 reads 4:20.
Conversion from 12-hour to 24-hour time: add 12 for p.m. hours, keep a.m. hours the same.12-hour clock → 24-hour clock1 p.m.→13:003 p.m.→15:006:45 p.m.→18:459:10 p.m.→21:1012 midnight→00:00p.m.: add 12a.m.: same

In the figure : For p.m. times add 12 to get the 24-hour time; a.m. times stay the same.

Rule 2: 12-hour to 24-hour — For p.m. add 12. For a.m. keep the same.

  • Easy : 3:00 p.m. = 3 + 12 = 15:00.
  • Medium : 9:05 p.m. = 21:05 and 18:45 = 6:45 p.m.
  • Exam-type : 12:30 a.m. = 00:30 and 12:15 p.m. = 12:15 (noon hour does not add 12).
Live figure

Reading the clock and 24-hour time

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

Open in the app
Remember

Midnight is 00:00 and noon is 12:00.

Common mistake

Writing 15:00 as 5 p.m. Subtract 12: 15 − 12 = 3 p.m.

Shortcut

Memory clue: After noon, add 12; for the clock back, subtract 12.

Spot the difference

12-hour24-hour
7:30 a.m.07:30
3:00 p.m.15:00
6:45 p.m.18:45

Practice questions

Easy
  1. 1The long hand is on 9. How many minutes past the hour?
  2. 2The long hand is on 8. How many minutes past the hour?
  3. 3Write 3:00 p.m. in 24-hour time.
Medium
  1. 4Write 9:05 p.m. in 24-hour time.
  2. 5Write 23:40 in 12-hour time.
  3. 6Write 12:30 a.m. in 24-hour time.
Challenging
  1. 7A train leaves at 18:45. At what time does it leave on a 12-hour clock?
  2. 8Ravi says 15:00 is 5 p.m. What is his mistake?
Show answers (try them yourself first)
  1. 145 minutes
  2. 240 minutes
  3. 315:00
  4. 421:05
  5. 511:40 p.m.
  6. 600:30
  7. 76:45 p.m.
  8. 815 − 12 = 3, so it is 3 p.m., not 5 p.m.

Calendar, months and leap year

From daily life

The month of your birthday may have 30 or 31 days, and February is shorter. The calendar tells the days of every month and shows how the weeks repeat.

Simple definition

A year has 12 months. January, March, May, July, August, October and December have 31 days; April, June, September and November have 30; February has 28. A leap year (लीप वर्ष) has 366 days, because February has 29.

The twelve months with their days: seven months of 31, four of 30 and February with 28 or 29.J31F28M31A30M31J30J31A31S30O31N30D31313028 (29 in leap year)

In the figure : Days in each month: 31, 30, or 28 (29 in a leap year).

Rule 1: Leap year rule — A year divisible by 4 is a leap year. A century year (like 1900) is a leap year only if divisible by 400.

  • Easy : 2024 ÷ 4 = 506, so 2024 is a leap year. 2026 is not (2026 ÷ 4 leaves 2).
  • Medium : 2000 is a leap year (divisible by 400) but 1900 and 2100 are not.
  • Exam-type : Days from January to March in an ordinary year: 31 + 28 + 31 = 90.

Rule 2: Weekdays repeat every 7 days — Divide the days by 7; the remainder tells how many days to move ahead.

  • Easy : If today is Thursday, 10 days later is Sunday (10 = 7 + 3).
  • Medium : If today is Monday, 20 days later is Sunday (20 = 14 + 6).
  • Exam-type : 5 weeks 3 days = 38 days. The weekday moves 3 ahead.
Remember

Leap year: February has 29 days. A year has 366 days.

Common mistake

Calling 2100 a leap year because 2100 is divisible by 4. It is a century year and 2100 is not divisible by 400.

Shortcut

Memory clue: Fist trick – knuckles are 31, dips are 30 (February is the short dip).

Spot the difference

YearLeap year?
2024Yes
2026No
2000Yes
2100No

Practice questions

Easy
  1. 1How many days are there in September?
  2. 2How many days are there in a leap year?
  3. 3Is 2028 a leap year?
Medium
  1. 4Is 2026 a leap year?
  2. 5Find the days from January to March in an ordinary year.
  3. 6Today is Thursday. What day will it be after 10 days?
Challenging
  1. 7Today is Monday. What day will it be after 20 days?
  2. 8Is 1900 a leap year? Give the reason.
Show answers (try them yourself first)
  1. 130
  2. 2366
  3. 3Yes, 2028 ÷ 4 = 507.
  4. 4No, 2026 ÷ 4 leaves remainder 2.
  5. 531 + 28 + 31 = 90
  6. 6Sunday
  7. 720 = 14 + 6, so Sunday.
  8. 8No. It is a century year and 1900 is not divisible by 400.

Elapsed time and duration

From daily life

Your school starts at 8:10 and the interval is at 10:30. How long is it from start to interval? The gap between two times is the time that has passed.

Simple definition

The time between a start and an end is the duration (कालावधी). To find the duration, count the hours first and then the minutes. To find the end time, add the duration. To find the start time, subtract the duration.

A time line from 10:20 to 12:50: add the hours first (2 hours to 12:20), then the minutes (30 more).10:2012:2012:50+ 2 hours+ 30 minTotal: 2 hours 30 minutes

In the figure : From 10:20 to 12:50: first 2 hours, then 30 minutes, so 2 hours 30 minutes.

Rule 1: Find the duration — Jump to the next full hour, then count hours, then the remaining minutes.

  • Easy : 9:30 a.m. to 12:15 p.m. = 2 hours 45 minutes.
  • Medium : 11:50 a.m. to 2:20 p.m. = 10 min + 2 h + 20 min = 2 hours 30 minutes.
  • Exam-type : 7:40 p.m. to 10:05 p.m. = 20 min + 2 h + 5 min = 2 hours 25 minutes.

Rule 2: Find the end or start time — Add the duration to the start; subtract it from the end.

  • Easy : A film from 5:30 p.m. for 2 h 15 min ends at 7:45 p.m.
  • Medium : A train leaves at 2:15 p.m. and takes 3 h 50 min. It reaches at 6:05 p.m.
  • Exam-type : A class ends at 9:10 a.m. after 1 h 40 min. It began at 7:30 a.m.
Remember

When minutes pass 60, change them into one more hour: 75 minutes = 1 hour 15 minutes.

Common mistake

Subtracting like ordinary numbers: 12:15 − 9:30 is not 3:85. Use hours and minutes with 60.

Shortcut

Memory clue: Hop to the hour, then hop to the end.

Spot the difference

To findDo
DurationCount hours then minutes
End timeStart + duration
Start timeEnd − duration

Practice questions

Easy
  1. 1Find the duration from 10:20 a.m. to 12:50 p.m.
  2. 2Find the duration from 9:30 a.m. to 12:15 p.m.
  3. 3Find the duration from 7:40 p.m. to 10:05 p.m.
Medium
  1. 4A film starts at 5:30 p.m. and runs for 2 h 15 min. When does it end?
  2. 5A journey starts at 10:45 a.m. and takes 75 minutes. When does it end?
  3. 6A class ends at 9:10 a.m. after 1 h 40 min. When did it start?
Challenging
  1. 7A train leaves at 2:15 p.m. and the journey takes 3 h 50 min. When does it reach?
  2. 8Sunil says 12:15 − 9:30 = 3:85. What is wrong? Give the right answer.
Show answers (try them yourself first)
  1. 12 hours 30 minutes
  2. 22 hours 45 minutes
  3. 32 hours 25 minutes
  4. 47:45 p.m.
  5. 512:00 noon
  6. 67:30 a.m.
  7. 76:05 p.m.
  8. 8Minutes never go above 59. The correct duration is 2 hours 45 minutes.

Time problems

From daily life

A cinema show, a bus timetable and a night's sleep are all time problems. We do them in small steps, changing everything to the same unit.

Simple definition

A time problem needs: (1) the same unit, (2) the right operation – add for later, subtract for earlier, multiply for repeats – and (3) a check on the clock.

Rule 1: Same unit first — Change hours and minutes to one unit before you add or multiply.

  • Easy : 5 songs of 4 minutes = 20 minutes.
  • Medium : 6 periods of 40 minutes = 240 minutes = 4 hours.
  • Exam-type : 6 days of 1 h 20 min homework = 6 × 80 = 480 minutes = 8 hours.

Rule 2: Repeated events and timetables — Keep adding the same gap.

  • Easy : A bus every 25 minutes from 8:00 goes at 8:00, 8:25, 8:50, 9:15.
  • Medium : A train leaves at 6:50 and takes 2 h 45 min. It reaches at 9:35.
  • Exam-type : 8 classes of 45 minutes = 360 minutes = 6 hours.
Remember

Check with the clock. Sleeping from 10 p.m. to 6 a.m. is 2 h to midnight + 6 h = 8 hours.

Common mistake

Mixing hours and minutes in one calculation. Convert first, then calculate.

Shortcut

Memory clue: Same unit – right sign – check.

Spot the difference

SituationOperation
Later timeAdd
Earlier timeSubtract
RepeatsMultiply

Practice questions

Easy
  1. 15 songs of 4 minutes play one after another. How long is that?
  2. 2A tap fills one bucket in 3 minutes. How long for 15 buckets?
  3. 3A bus goes at 8:00 and then every 25 minutes. Write the first four times.
Medium
  1. 4A shop has 8 classes of 45 minutes. How many hours?
  2. 5A train leaves at 6:50 and takes 2 h 45 min. When does it reach?
  3. 6Sleeping from 10 p.m. to 6 a.m. – how many hours?
Challenging
  1. 7A shop opens at 9:30 a.m. and closes at 8:15 p.m. For how long is it open?
  2. 8A film starts at 4:50 p.m. and ends at 7:05 p.m. Find its duration and say how many minutes it is.
Show answers (try them yourself first)
  1. 120 minutes
  2. 245 minutes
  3. 38:00, 8:25, 8:50, 9:15
  4. 4360 minutes = 6 hours
  5. 59:35
  6. 62 + 6 = 8 hours
  7. 710 hours 45 minutes
  8. 82 hours 15 minutes = 135 minutes.