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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
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B
8:461011
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C
8:45711
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D
8:40411
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Solution

The correct option is D 8:40411
60 minutes or 1 hour = 360°
Each minute → 36060=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 =2225.5=40411 minutes

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