Discussion

How much does a clock lose per day, if its hands coincide ever 65 minutes ?

Answer: A

In a correct clock the hands coincide every

\[ \frac{720}{11} = 65\tfrac{5}{11} \text{ minutes} \]

Here they take 65 minutes, slightly less, so the clock is running fast - and the conventional measure of the discrepancy is

\[ \frac{720}{11} - 65 = \frac{5}{11} \text{ minutes per interval} \]

There are \( \tfrac{1440}{65} \) such intervals in a day:

\[ \frac{5}{11} \times \frac{1440}{65} = \frac{7200}{715} = \frac{1440}{143} \text{ minutes} \]

That is about 10.07 minutes - a much smaller discrepancy than the 64-minute case, because 65 is far closer to \( 65\tfrac{5}{11} \).

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