RBSE Solutions Class 5 Maths Chapter 11 Time Exercise 11.1

Question 1. Convert the time units of following questions,
(i) \( 10\frac {3}{5} \) hour = minute
(ii) \( 2\frac {1}{4} \) hour = seconds
(iii) \( \frac {1}{5} \) minute = seconds
(iv) \( 1\frac {2}{3} \) minute = seconds
Answer:
(i) \( 10\frac {3}{5} \) hour = 10 hours + \( \frac {3}{5} \) hour
= \( 10 \times 60 \) minutes + \( \frac {3}{5} \times 60 \) minutes
= 600 minutes + \( 3 \times 12 \) minutes
= 600 minutes + 36 minutes
= 636 minutes
(ii) \( 2\frac {1}{4} \) hour = 2 hours + \( \frac {1}{4} \) hour
= \( 2 \times 60 \) minutes + \( \frac {1}{4} \times 60 \) minutes
= 120 minutes + 15 minutes
= \( 120 \times 60 \) seconds + \( 15 \times 60 \) seconds
= 7200 seconds + 900 seconds
= 8100 seconds
(iii) \( \frac {1}{5} \) minute = \( \frac {1}{5} \times 60 \) seconds = 12 seconds
(iv) \( 1\frac {2}{3} \) minute = 1 minute + \( \frac {2}{3} \) minute
= \( 1 \times 60 \) seconds + \( \frac {2}{3} \times 60 \) seconds
= 60 seconds + \( 2 \times 20 \) seconds
= 60 seconds + 40 seconds
= 100 seconds
In simple words: To change units, multiply hours by 60 to get minutes, and minutes by 60 to get seconds. Always break down mixed numbers into whole and fractional parts first.

🎯 Exam Tip: Remember the basic conversions: 1 hour = 60 minutes, and 1 minute = 60 seconds. This is key for all time unit conversions.

Question 2. Add the following time units:
(i) 2 hours 42 minutes + 4 hours 10 minutes
(ii) 10 minutes 50 seconds + 8 minutes 20 seconds
(iii) 4 hours 25 minutes 45 seconds + 7 hours 12 minutes 5 seconds
(iv) 9 hours 36 minutes 2 seconds + 5 hours 40 minutes 52 seconds
Answer:
(i)
  2 hours 42 minutes
+ 4 hours 10 minutes
  6 hours 52 minutes
To add time, first add the minutes together, then add the hours together. Since 52 minutes is less than 60, no carrying over is needed here.
(ii)
  10 minutes 50 seconds
+ 8 minutes 20 seconds
  18 minutes 70 seconds
Since 70 seconds is more than 60 seconds, we convert 60 seconds to 1 minute.
  18 minutes + 1 minute (from 60 seconds) + 10 seconds
= 19 minutes 10 seconds
First, add the seconds. If the total seconds are 60 or more, convert 60 seconds into 1 minute and add it to the minute total. Then add the minutes. This is how we carry over time units.
(iii)
  4 hours 25 minutes 45 seconds
+ 7 hours 12 minutes 5 seconds
  11 hours 37 minutes 50 seconds
Add the seconds, then the minutes, and finally the hours. Since all totals are less than 60 for minutes and seconds, no carrying over is required in this sum. This makes the addition straightforward.
(iv)
  9 hours 36 minutes 2 seconds
+ 5 hours 40 minutes 52 seconds
  14 hours 76 minutes 54 seconds
Since 76 minutes is more than 60 minutes, we convert 60 minutes to 1 hour.
  14 hours + 1 hour (from 60 minutes) + 16 minutes 54 seconds
= 15 hours 16 minutes 54 seconds
First add the seconds, then the minutes, and finally the hours. Since 76 minutes is more than 60, convert 60 minutes into 1 hour and add it to the total hours. This process ensures the minutes part stays under 60.
In simple words: When adding time, add seconds with seconds, minutes with minutes, and hours with hours. If seconds or minutes go over 60, carry over 1 minute or 1 hour to the next unit.

🎯 Exam Tip: Always remember to carry over 60 seconds as 1 minute, and 60 minutes as 1 hour when adding time, similar to how you carry over in normal addition.

Question 3. Subtraction
(i) 9 hours 32 minutes from 12 hours 18 minutes
(ii) 25 minutes 49 seconds from 29 minutes 39 seconds
(iii) 7 hours 35 minutes from 14 hours 8 minutes
(iv) 10 hours 50 minutes from 20 hours 40 minutes
Answer:
(i)
  12 hours 18 minutes
- 9 hours 32 minutes
We cannot subtract 32 minutes from 18 minutes. So, we borrow 1 hour (60 minutes) from 12 hours. This makes 12 hours become 11 hours, and 18 minutes become \( 18 + 60 = 78 \) minutes.
  11 hours 78 minutes
- 9 hours 32 minutes
  2 hours 46 minutes
To subtract, first check if minutes can be subtracted. If not, borrow 1 hour (60 minutes) from the hours. This makes the minutes sufficient for subtraction, leading to a correct result.
(ii)
  29 minutes 39 seconds
- 25 minutes 49 seconds
We cannot subtract 49 seconds from 39 seconds. So, we borrow 1 minute (60 seconds) from 29 minutes. This makes 29 minutes become 28 minutes, and 39 seconds become \( 39 + 60 = 99 \) seconds.
  28 minutes 99 seconds
- 25 minutes 49 seconds
  3 minutes 50 seconds
First, check if seconds can be subtracted. If not, borrow 1 minute (60 seconds) from the minutes. This ensures that the subtraction can be carried out smoothly and accurately.
(iii)
  14 hours 8 minutes
- 7 hours 35 minutes
We cannot subtract 35 minutes from 8 minutes. So, we borrow 1 hour (60 minutes) from 14 hours. This makes 14 hours become 13 hours, and 8 minutes become \( 8 + 60 = 68 \) minutes.
  13 hours 68 minutes
- 7 hours 35 minutes
  6 hours 33 minutes
First, check if minutes can be subtracted. If not, borrow 1 hour (60 minutes) from the hours. This step is essential for accurate time calculations when the smaller unit is less than the amount to be subtracted.
(iv)
  20 hours 40 minutes
- 10 hours 50 minutes
We cannot subtract 50 minutes from 40 minutes. So, we borrow 1 hour (60 minutes) from 20 hours. This makes 20 hours become 19 hours, and 40 minutes become \( 40 + 60 = 100 \) minutes.
  19 hours 100 minutes
- 10 hours 50 minutes
  9 hours 50 minutes
First, check if minutes can be subtracted. If not, borrow 1 hour (60 minutes) from the hours. This technique is a cornerstone of correctly performing time-based subtractions.
In simple words: When subtracting time, start from the smallest unit (seconds, then minutes). If you cannot subtract a smaller unit, borrow 60 from the next bigger unit (e.g., 60 seconds from minutes, 60 minutes from hours).

🎯 Exam Tip: Clearly show your borrowing steps. Cross out the original numbers and write the new, adjusted numbers above them to avoid errors.

Question 4. If a student studies for 5 hours 30 minutes at school and then studies for 3 hours 45 minutes at home, what is the total time they spent studying?
Answer:
Time spent at school = 5 hours 30 minutes
Time spent at home = 3 hours 45 minutes
Total study time = 5 hours 30 minutes + 3 hours 45 minutes
  5 hours 30 minutes
+ 3 hours 45 minutes
  8 hours 75 minutes
Since 75 minutes is more than 60 minutes, we convert 60 minutes to 1 hour.
75 minutes = 1 hour 15 minutes
So, 8 hours 75 minutes = 8 hours + 1 hour 15 minutes = 9 hours 15 minutes.
To find the total study time, first add the hours and minutes separately. The total minutes (75) are more than 60, so convert 60 minutes into 1 hour and add it to the total hours. This way, the total time is expressed in the standard hour and minute format.
In simple words: Add the hours and minutes separately. If the total minutes are more than 60, turn 60 minutes into 1 extra hour and add it to the hour total.

🎯 Exam Tip: Always simplify your answer so that the minutes are less than 60 and seconds are less than 60. This is the standard way to express time.

Question 5. The distance between Dholpur and Bharatpur is 90 kilometers. Rakesh takes just 2 hours 12 minutes to complete this distance by car and Firoj takes 3 hours 8 minutes by motorcycle. Find out the extra time taken by Firoj as compared to Rakesh.
Answer:
Time taken by Firoj = 3 hours 8 minutes
Time taken by Rakesh = 2 hours 12 minutes
Extra time taken by Firoj = Time taken by Firoj - Time taken by Rakesh
  3 hours 8 minutes
- 2 hours 12 minutes
We cannot subtract 12 minutes from 8 minutes. So, we borrow 1 hour (60 minutes) from Firoj's time.
3 hours 8 minutes becomes 2 hours \( 8 + 60 \) minutes = 2 hours 68 minutes.
Now, subtract:
  2 hours 68 minutes
- 2 hours 12 minutes
  0 hours 56 minutes
So, Firoj took 56 minutes extra.
To find the extra time Firoj took, subtract Rakesh's time from Firoj's time. Since 12 minutes cannot be subtracted from 8 minutes, we borrow 1 hour (60 minutes) from Firoj's 3 hours. This makes Firoj's time 2 hours and 68 minutes. Then, subtract the hours and minutes. This comparison clearly shows the difference in travel time.
In simple words: To find the difference in time, subtract the smaller time from the larger time. If needed, borrow 1 hour (60 minutes) from the hours to complete the subtraction in minutes.

🎯 Exam Tip: When solving word problems, first identify what needs to be calculated (e.g., total time, difference in time) and then choose the correct operation (addition or subtraction).

Question 6. Identify True and False.
(i) We divide a minute by 60 to convert into seconds (Correct/False)
(ii) One hour has 3600 seconds. (Correct/False)
(iii) The time taken by the minute hand to travel sixty small parts is equal to the time taken by the hour hand to travel a big part. (Correct/False)
(iv) Half hour is equal to 15 minutes. (Correct/False)
Answer:
(i) False
To convert minutes into seconds, you actually multiply by 60, not divide. Dividing would make the number smaller, which is incorrect when going from a larger unit to a smaller one.
(ii) True
One hour has 60 minutes, and each minute has 60 seconds. So, 60 minutes multiplied by 60 seconds equals 3600 seconds in total. This conversion is a fundamental time fact.
(iii) True
When the minute hand travels 60 small parts (which is one full circle or 60 minutes), the hour hand moves from one big number to the next (which is one hour). This shows the synchronized movement of clock hands.
(iv) False
A full hour has 60 minutes. Therefore, half of an hour would be 60 divided by 2, which equals 30 minutes, not 15 minutes. Understanding these basic time divisions is important.
In simple words: Remember that 60 seconds make a minute, and 60 minutes make an hour. Half an hour is 30 minutes. Use these basic facts to check True or False statements.

🎯 Exam Tip: Always double-check your knowledge of basic time conversions (seconds to minutes, minutes to hours) before answering True/False questions related to them.