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

132 ⁸/₁₁ min.
236 ⁵/₁₁ min.
390 min.
496 min.

Answer:- 1

Explanation:-

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}

$\eqalign{ & 55\,\min .\,{\text{spaces}}\,{\text{are}}\,{\text{covered}}\,{\text{in}}\,60\,\min \cr & 60\,\min .\,{\text{spaces}}\,{\text{are}}\,{\text{covered}}\,{\text{in}} \cr & = \left( {\frac{{60}}{{55}} \times 60} \right)\,\min . \cr & = 65\frac{5}{{11}}\,\min . \cr & {\text{Loss}}\,{\text{in}}\,64\,\min . \cr & = \left( {65\frac{5}{{11}} - 64} \right) = \frac{{16}}{{11}}\,\min . \cr & {\text{Loss}}\,{\text{in}}\,24\,hrs \cr & = \left( {\frac{{16}}{{11}} \times \frac{1}{{64}} \times 24 \times 60} \right)\,\min \cr & = 32\frac{8}{{11}}\,\min \cr}$