Question

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?

• A. 14 min 10 s lost
• B. 13 min 50 s lost
• C. 13 min 20 s gained
• D. 14 min 40 s gained

Hint:

For clock problems, use relative speed of hands: $5.5^\circ$/min.

Answer 1

The Correct Option is A

True time between every 3rd crossing = $3 \times \frac{12}{11}$ hrs = $\frac{36}{11}$ hrs = 3 hr 16 min 21.8 s. Watch shows 3 hr 18 min 15 s → running slow. Loss per interval = 1 min 53.2 s. Number of such intervals per day = $\frac{24}{36/11} = 7\frac{1}{3}$. Total loss ≈ $7.33 \times 1.887$ min ≈ 13.83 min ≈ 14 min 10 s.