Question

Between 8 am and 9 am, the minute hand of a clock will lag behind the hour hand by 3 minutes at:

• A. 8: 42
• B. $8:46\frac{10}{11}$
• C. $8:45\frac{7}{11}$
• D. $8:40\frac{4}{11}$

Answer 1

The correct option is D $8:40\frac{4}{11}$

60 minutes or 1 hour = 360°
Each minute → $\frac{360}{60}=6°$
A minute hand sweeps 6° every minute, while the hour hand moves 360° in 12 hours (720 min).
So, every minute the hour hand sweeps → 0.5°
Difference = 6 - 0.5 = 5.5°
So, every minute the minute hand covers 5.5° more than the hour hand.
At 8 am, the hands are 240° apart. Now, we need to find the time at which the minute hand has to lag behind the hour hand by 3 minutes → 18°
The difference must decrease by = 240 - 18 = 222°
Which means the minute hand has to cover 222°
Time taken will be $=\frac{222}{5.5}=40\frac{4}{11}$ minutes