Between 6 pm and 7 pm, the minute hand of a clock will be ahead of the hour hand by 3 minutes at:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6:36 pm
The dial has 60 minute spaces. The minute hand moves 60 spaces in an hour and the hour hand only 5, so the minute hand gains \(\frac{55}{60}=\frac{11}{12}\) of a minute space every minute.
At 6:00 the hour hand is at the 6, so it is 30 minute spaces ahead of the minute hand at the 12
To be 3 spaces ahead of the hour hand, the minute hand must first catch up 30 spaces and then go 3 more: \(30+3=33\) spaces
Time needed \(\displaystyle =33\div\frac{11}{12}=33\times\frac{12}{11}=36\) minutes
So the time is 36 minutes past 6, that is, 6:36 pm
