[32 \dfrac{8}{11} min.] How much does a watch lose per day, if its hands coincide every 64 minutes?

For Competitive Exams

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

32$ \dfrac{8}{11} $min.

36$ \dfrac{5}{11} $min.

90 min.

96 min.

Explanation:

60 min. spaces are covered in$ \left(\dfrac{60}{55} \times 60\right) $min.= 65$ \dfrac{5}{11} $min.

Loss in 64 min. =$ \left(65\dfrac{5}{11} - 64\right) $=$ \dfrac{16}{11} $min.

Loss in 24 hrs =$ \left(\dfrac{16}{11} \times\dfrac{1}{64} \times 24 \times 60\right) $min.=32$ \dfrac{8}{11} $min.

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