Discussion
How much does a watch lose per day, if its hands coincide ever 64 minutes?
Answer: A
In a correct clock the hands coincide every
\[ \frac{720}{11} = 65\tfrac{5}{11} \text{ minutes} \]
Here they take 64 minutes, less than they should, so the watch is running fast - but the question asks how much it loses, and the conventional treatment measures the shortfall of the interval:
\[ \frac{720}{11} - 64 = \frac{16}{11} \text{ minutes per interval} \]
\[ \frac{16}{11} \times \frac{1440}{64} = \frac{23040}{704} = 32\tfrac{8}{11} \text{ minutes a day} \]
The 24-hour figure comes from the number of coincidence intervals in a day, \( \tfrac{1440}{64} = 22.5 \).
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