A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the correct time at 9 AM on 11th July

Q. A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the correct time at 9 AM on 11^th July. What will be the correct time to the nearest minute when the clock shows 2 PM on 15^th July of the same year?

Ans: 12:58 PM

Sol:

Minutes gained in every 24 hours = 15 = 0.25 hour

⇒ every 1 hour, 1/96 hours are gained.

When the clock shows 2 PM on 15th July of the same year, let’s assume x hours are spent in an error-free clock.

So for x hours, the gain will be x/96 = 0.0104x

So, the total time gone in the faulty clock will be x + 0.0104x = 1.0104x

The total time spent on the faulty clock is given by  

No. of hours between 9 AM on 11th July and 2 PM on 15th July = 24 × 4 + 5 = 101

Now, equating both

1.0104x = 101 ⇒ x = 99.96 hours

So the correct time spent is 99.96 hours = 4 days + 3 + 0.96 hours

⇒ 4 days + 3 hrs + 57.62 min

Calculating from 9 AM, 11th July, the correct time to the nearest minute = approximately 12.58 PM.