Question

Select the correct alternative from the given choices.

The minute-hand of a clock overtakes the hour-hand at intervals of 62 minutes of a correct time. How much in a day does the clock gain or losse?

• A. $80\frac{80}{341}minutes$
• B. $850\frac{90}{311}minutes$
• C. $80\frac{70}{341}minutes$
• D. $80\frac{60}{341}minutes$

Answer 1

The correct option is A $80\frac{80}{341}minutes$

In a correct clock, the hands of a clock coincide every $65\frac{5}{11}$ minutes. But in this case both the hands are together again after 62 minutes, hence the clock gains time.
Gain in $62minutes=(65\frac{5}{11}-62)=3\frac{5}{11}min$ gain.
Gain in 24 hours $=38/11\times 60\times 24/62$
$=\frac{19\times 60\times 24}{11\times 31}=80\frac{80}{341}$
So the clock gains $80\frac{80}{341}$ minutes in 24 hours.