Racing Seconds — NCERT Solutions

Note: The answer depends on the two clock images.

Method: Find the difference in the positions of the seconds hands on both clocks.

Example: If the seconds hand moved from 12 to 6 (i.e., 30 seconds), then Raghu took 30 seconds. (Read the exact value from your textbook clocks.)

Given: Raghu took 20 seconds.

On a clock, the seconds hand completes a full circle (360°) in 60 seconds.

In 20 seconds, the seconds hand moves:
$$\frac{20}{60} \times 360° = 120°$$

This means the seconds hand moves from 12 to the 4 (since each number on the clock represents 5 seconds, and $20 \div 5 = 4$).

Draw the seconds hand pointing to the 4 on the clock.

Given: Rani took 30 seconds.

In 30 seconds, the seconds hand moves:
$$\frac{30}{60} \times 360° = 180°$$

This means the seconds hand moves from 12 to the 6 (since $30 \div 5 = 6$).

Draw the seconds hand pointing to the 6 on the clock.

Given: Raghav took 60 seconds.

In 60 seconds, the seconds hand completes one full circle:
$$\frac{60}{60} \times 360° = 360°$$

This means the seconds hand returns to the 12 (same position as the start).

Draw the seconds hand pointing to the 12 on the clock.

Given: Ritu took 40 seconds.

In 40 seconds, the seconds hand moves:
$$\frac{40}{60} \times 360° = 240°$$

This means the seconds hand moves from 12 to the 8 (since $40 \div 5 = 8$).

Draw the seconds hand pointing to the 8 on the clock.

Formula used: $1 \text{ hour} = 60 \text{ minutes}$

(i) 1 hour 10 minutes = ____ minutes
$$1 \times 60 + 10 = 60 + 10 = \mathbf{70} \text{ minutes}$$

(ii) 2 hours 45 minutes = ____ minutes
$$2 \times 60 + 45 = 120 + 45 = \mathbf{165} \text{ minutes}$$

(iii) 3 hours 15 minutes = ____ minutes
$$3 \times 60 + 15 = 180 + 15 = \mathbf{195} \text{ minutes}$$

(iv) 4 hours 20 minutes = ____ minutes
$$4 \times 60 + 20 = 240 + 20 = \mathbf{260} \text{ minutes}$$

(v) 75 minutes = ____ hour ____ minutes
$$75 \div 60 = 1 \text{ hour remainder } 15 \text{ minutes}$$
$$= \mathbf{1} \text{ hour } \mathbf{15} \text{ minutes}$$

(vi) 150 minutes = ____ hours ____ minutes
$$150 \div 60 = 2 \text{ hours remainder } 30 \text{ minutes}$$
$$= \mathbf{2} \text{ hours } \mathbf{30} \text{ minutes}$$

(vii) 220 minutes = ____ hours ____ minutes
$$220 \div 60 = 3 \text{ hours remainder } 40 \text{ minutes}$$
$$(3 \times 60 = 180, \; 220 - 180 = 40)$$
$$= \mathbf{3} \text{ hours } \mathbf{40} \text{ minutes}$$

(viii) 390 minutes = ____ hours ____ minutes
$$390 \div 60 = 6 \text{ hours remainder } 30 \text{ minutes}$$
$$(6 \times 60 = 360, \; 390 - 360 = 30)$$
$$= \mathbf{6} \text{ hours } \mathbf{30} \text{ minutes}$$

Formula used: $1 \text{ minute} = 60 \text{ seconds}$

(i) 320 sec = ___ min ___ sec
$$320 \div 60 = 5 \text{ min remainder } 20 \text{ sec}$$
$$(5 \times 60 = 300, \; 320 - 300 = 20)$$
$$= \mathbf{5} \text{ min } \mathbf{20} \text{ sec}$$

(ii) 225 sec = ___ min ___ sec
$$225 \div 60 = 3 \text{ min remainder } 45 \text{ sec}$$
$$(3 \times 60 = 180, \; 225 - 180 = 45)$$
$$= \mathbf{3} \text{ min } \mathbf{45} \text{ sec}$$

(iii) 700 sec = ___ min ___ sec
$$700 \div 60 = 11 \text{ min remainder } 40 \text{ sec}$$
$$(11 \times 60 = 660, \; 700 - 660 = 40)$$
$$= \mathbf{11} \text{ min } \mathbf{40} \text{ sec}$$

(iv) 1,000 sec = ___ min ___ sec
$$1000 \div 60 = 16 \text{ min remainder } 40 \text{ sec}$$
$$(16 \times 60 = 960, \; 1000 - 960 = 40)$$
$$= \mathbf{16} \text{ min } \mathbf{40} \text{ sec}$$

(v) 10 min 13 sec = ___ sec
$$10 \times 60 + 13 = 600 + 13 = \mathbf{613} \text{ sec}$$

(vi) 4 min 8 sec = ___ sec
$$4 \times 60 + 8 = 240 + 8 = \mathbf{248} \text{ sec}$$

(vii) 15 min 40 sec = ___ sec
$$15 \times 60 + 40 = 900 + 40 = \mathbf{940} \text{ sec}$$

Given: Time taken for each subject = 50 minutes
Number of subjects = 4

Total time = $4 \times 50 = 200$ minutes

Converting to hours and minutes:
$$200 \div 60 = 3 \text{ hours remainder } 20 \text{ minutes}$$
$$(3 \times 60 = 180, \; 200 - 180 = 20)$$

Total time taken = 3 hours 20 minutes.

Given: Departure time = 08:00 hours, Arrival time = 09:05 hours

Step 1: From 08:00 to 09:00 = 1 hour
Step 2: From 09:00 to 09:05 = 5 minutes

Total time = 1 hour + 5 minutes

Raghu took 1 hour 5 minutes to reach his Nana ji's house.

Given: Start time = 06:15 PM, Duration = 1 hour 45 minutes

Step 1: Add 1 hour to 06:15 PM → 07:15 PM
Step 2: Add 45 minutes to 07:15 PM → 07:15 + 45 min

$15 + 45 = 60$ minutes = 1 hour

So 07:15 PM + 45 minutes = 08:00 PM

Jyoti reached home at 08:00 PM.

Given: Finish time = 09:40 PM, Duration = 1 hour 10 minutes

To find start time, subtract the duration from the finish time.

Step 1: Subtract 10 minutes from 09:40 PM → 09:30 PM
Step 2: Subtract 1 hour from 09:30 PM → 08:30 PM

Ragini started her homework at 08:30 PM.

Given: Departure time = 08:30 AM, Duration = 4 hours 10 minutes

Step 1: Add 4 hours to 08:30 AM → 12:30 PM
Step 2: Add 10 minutes to 12:30 PM → 12:40 PM

The children returned at 12:40 PM.

Given: Start time = 06:00 PM, Duration = 1 hour 30 minutes

Step 1: Add 1 hour to 06:00 PM → 07:00 PM
Step 2: Add 30 minutes to 07:00 PM → 07:30 PM

Raji finished her homework at 07:30 PM.

Given: Start time = 05:30 PM, Duration = 1 hour 10 minutes

Step 1: Add 1 hour to 05:30 PM → 06:30 PM
Step 2: Add 10 minutes to 06:30 PM → 06:40 PM

Alya comes back at 06:40 PM.

Given: Start time = 12:30 PM, Duration = 35 minutes

Adding 35 minutes to 12:30 PM:
$$30 + 35 = 65 \text{ minutes} = 1 \text{ hour } 5 \text{ minutes}$$

So: 12:30 PM + 35 minutes = 12:00 PM + 1 hour 5 minutes = 01:05 PM

The lunch break will end at 01:05 PM.

Given: Current time = 08:35 PM, Duration = 8 hours 25 minutes

Step 1: Add 8 hours to 08:35 PM
$$08:35 \text{ PM} + 8 \text{ hours} = 04:35 \text{ AM (next day)}$$
(Since 8 PM + 4 hours = 12 AM midnight, then + 4 more hours = 4:35 AM)

Step 2: Add 25 minutes to 04:35 AM
$$35 + 25 = 60 \text{ minutes} = 1 \text{ hour}$$
$$04:35 \text{ AM} + 25 \text{ minutes} = 05:00 \text{ AM}$$

After 8 hours and 25 minutes, it will be 05:00 AM (next day).