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

Option :

Explanation:

Solution:
$\begin{array}{rl}& 55\phantom{\rule{thinmathspace}{0ex}}min.\phantom{\rule{thinmathspace}{0ex}}\text{spaces}\phantom{\rule{thinmathspace}{0ex}}\text{are}\phantom{\rule{thinmathspace}{0ex}}\text{covered}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}60\phantom{\rule{thinmathspace}{0ex}}min\\ & 60\phantom{\rule{thinmathspace}{0ex}}min.\phantom{\rule{thinmathspace}{0ex}}\text{spaces}\phantom{\rule{thinmathspace}{0ex}}\text{are}\phantom{\rule{thinmathspace}{0ex}}\text{covered}\phantom{\rule{thinmathspace}{0ex}}\text{in}\\ & =\left(\frac{60}{55}×60\right)\phantom{\rule{thinmathspace}{0ex}}min.\\ & =65\frac{5}{11}\phantom{\rule{thinmathspace}{0ex}}min.\\ & \text{Loss}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}64\phantom{\rule{thinmathspace}{0ex}}min.\\ & =\left(65\frac{5}{11}-64\right)=\frac{16}{11}\phantom{\rule{thinmathspace}{0ex}}min.\\ & \text{Loss}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}24\phantom{\rule{thinmathspace}{0ex}}hrs\\ & =\left(\frac{16}{11}×\frac{1}{64}×24×60\right)\phantom{\rule{thinmathspace}{0ex}}min\\ & =32\frac{8}{11}\phantom{\rule{thinmathspace}{0ex}}min\end{array}$