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1. How much does a watch lose per day, if its hands coincide every 64 minutes?

A. $32 \frac{8}{11}$ min.

B. $36 \frac{5}{11}$ min.

C. 90 min.

D. 96 min.

Solution:

\begin{aligned} 55 min . spaces are covered in 60 min \\ 60 min . spaces are covered in \\ = (\frac{60}{55} \times 60) min . \\ = 65 \frac{5}{11} min . \\ Loss in 64 min . \\ = 65 \frac{5}{11} - 64 = \frac{16}{11} min . \\ Loss in 24 h r s . \\ = (\frac{16}{11} \times \frac{1}{64} \times 24 \times 60) min . \\ = 32 \frac{8}{11} min . \end{aligned}

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