Question

The minute and hour hands of a clock overlap every 60 minutes of correct time. How much does the clock lose or gain in a day?

• A. $130\frac{10}{11}$ minutes
• B. $58\frac{6}{7}$ minutes
• C. $143\frac{5}{11}$ minutes
• D. $139\frac{4}{11}$ minutes
• E. None of these

Answer 1

The correct option is A $130\frac{10}{11}$ minutes

In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.

To be together again, the minute hand must gain 60 minutes over the hour hand.

55 minutes are gained in 60 min.

60 min. are gained in [(60/55) * 60] min = $65\frac{5}{11}$min.

Therefore, loss in 60 minutes = $65\frac{5}{11}-60=5\frac{5}{11}$ min.

Loss in 24 hours = $5\frac{5}{11}\ast \frac{24\ast 60}{60}$ = $130\frac{10}{11}$min.

Therefore, the clock loses $130\frac{10}{11}$ minutes in 24 hours.