Imagine that your watch was correct at noon, but then it began to lose 30 minutes each hour. It now shows at 4 P.M. but it stopped 5 hours ago. What is the correct time now ?

Correct option is A

Solution:

Step 1: Understand the situation

If the watch shows 4 P.M., it has lost time due to its faulty behavior. The time it stopped at is 4 P.M., but the actual time elapsed since noon must be more than 4 hours.
Since the watch loses 30 minutes per hour, the actual time that has elapsed is calculated by accounting for the loss.

Step 2: Relationship between actual time and faulty time

Let the actual elapsed time since noon be t hours. During this period, the faulty watch loses 30 minutes per hour, meaning the faulty elapsed time is:

Faulty elapsed time = t - (t / 2) = t / 2 hours.

The faulty elapsed time from noon to 4 P.M. is 4 hours:

t / 2 = 4 ⟹ t = 8 hours.

Thus, the actual time elapsed since noon when the watch showed 4 P.M. is 8 hours.

Step 3: Account for the 5 hours when the watch was stopped

If the watch stopped 5 hours ago, the actual elapsed time since noon is:

8 + 5 = 13 hours.

Adding 13 hours to noon gives the correct time:

12:00 P.M. + 13 hours = 1:00 A.M.

Final Answer:

1:00 A.M.