In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hr 18 min and 15 s of watch time. What is the time gained or lost by this watch in one day?

1. 13 min 50 s lost
2. 14 min 40 s gained
3. 14 min 10 s lost
4. 13 min 20 s gained

Answer

In a watch that is running correct, the minute hand should cross the hour hand once in every 65 + 5/11 minutes.

So, they should ideally cross three times once in 3 x 720/11 min = 196.36 min.

But in the watch under consideration, they meet after every 3 hr, 18 min and 15 s, i.e. (3 × 60 + 18 + 15/60) min = 198.25 min.

In other words, the watch is actually losing time (as it is slower than the normal watch). Hence, when the watch elapsed 198.25 min, it actually should have elapsed 196.36 min. So in a day, when watch will elapse (60 × 24) = 1440, it should actually elapse (1440 x 196.36/198.25) = 1426.27.

Hence, the amount of time lost in one day = (1440 - 1426.27) = 13.73, i.e. 13 min and 50 s (approximately).

The correct option is A.