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 11th July. What will be the correct time to the nearest minute when the clock shows 2 PM on 15th July of the same year?
(A) 12:45 PM | (B) 12:58 PM | (C) 1:00 PM | (D) 2:00 PM |
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.