LR - Clocks - Previous Year CAT/MBA Questions

Answer: Option B

Explanation :

In a watch that is running correct, the minute hand should cross the hour hand once in every 65 + $\frac{5}{11}$ min. So they should ideally cross three times once in $3\times \left(\frac{720}{11}\right)=\frac{2060}{11}$ 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 + $\frac{15}{60}$) = $\frac{793}{4}$ min = 198.25 min. In other words, our watch is actually losing time (as it is slower than the normal watch). Hence, when our watch elapsed 198.25 min, it actually should have elapsed 196.36 min. So in a day, when our watch will elapse (60 × 24) = 1440, it should actually elapse $\left(1440\times \frac{196.36}{198.25}\right)$ = 1426. 27. Hence, the amount of time lost by our watch in one day = (1440 – 1426.27) = 13.73, i.e. 13 min and 50 s (approximately).