A defective watch showed the weird behaviour. It gains 5 seconds per 3 minutes for first hour, loss 10 seconds per 3 minutes in the second hour, again gains 15 seconds per 3 minutes for next one hour and so on. The watch showed the correct time at 7:00 A.M. What time it indicated at 7:00 P.M.?a)6:50 P.M.b)7:00 P.M.c)7:10 P.M.d)7:20 P.M.Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Given Information:
A defective watch showed the following behaviour:
- It gains 5 seconds per 3 minutes for the first hour.
- It loses 10 seconds per 3 minutes in the second hour.
- It gains 15 seconds per 3 minutes for the next one hour.
- The watch showed the correct time at 7:00 A.M.

To find:
What time did the watch indicate at 7:00 P.M.?

Solution:
Let's calculate the net gain or loss in seconds per minute due to the watch's behaviour in one cycle of 3 hours:
- In the first hour, the watch gains 5/3 seconds per minute.
- In the second hour, the watch loses 10/3 seconds per minute.
- In the third hour, the watch gains 15/3 or 5 seconds per minute.
- Therefore, the net gain or loss in one cycle of 3 hours is (5/3 - 10/3 + 5) = 0 seconds per minute.

This means that the watch shows the correct time after every cycle of 3 hours.

Now, we know that the watch showed the correct time at 7:00 A.M. This means that the time indicated by the watch after every cycle of 3 hours will be a multiple of 3 hours from 7:00 A.M.

So, to find the time indicated by the watch at 7:00 P.M., we need to calculate the number of cycles of 3 hours between 7:00 A.M. and 7:00 P.M.

- Number of hours between 7:00 A.M. and 7:00 P.M. = 12 hours.
- Number of cycles of 3 hours in 12 hours = 12/3 = 4.

So, the time indicated by the watch after 4 cycles of 3 hours from 7:00 A.M. will be the correct time.

Let's calculate the gain or loss in seconds due to the watch's behaviour in these 4 cycles:
- In the first cycle, the watch gains 5 seconds per 3 minutes or 100 seconds in 1 hour.
- In the second cycle, the watch loses 10 seconds per 3 minutes or 200 seconds in 1 hour.
- In the third cycle, the watch gains 15 seconds per 3 minutes or 300 seconds in 1 hour.
- In the fourth cycle, the watch loses 10 seconds per 3 minutes or 200 seconds in 1 hour.

So, the net gain or loss in these 4 cycles of 3 hours is (100 - 200 + 300 - 200) = 0 seconds.

This means that the time indicated by the watch after 4 cycles of 3 hours from 7:00 A.M. will be the correct time, which is 7:00 P.M.

Therefore, the answer is option 'A', i.e. 6:50 P.M.

Answer

Therefore in 12 hours from 7:00 Am − 7:00 PM
100 − 200 + 300 - 400 + 500 - 600 + 700 -800 +900 -1000 +1000 − 1200
⇒ (−600 sec)
i.e. 10 min lose ⇒ 6 : 50 PM

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