At what time, between 3 o'clock and 4 o'clock, both the hands will coincide with each other?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(16 \frac{4}{11}\) minutes
The minute hand moves 6° a minute and the hour hand 0.5° a minute, so the minute hand gains 5.5° on the hour hand every minute. The hands coincide when the minute hand has made up the gap between them.
At 3 o’clock the hour hand is on the 3, that is, \(3\times30=90^{\circ}\) ahead of the minute hand
Time to gain 90° \(\displaystyle =\frac{90}{5.5}=\frac{180}{11}=16\frac{4}{11}\) minutes past 3
