Question

How much does a watch gain or lose per day, if it's hands coincide every $64$ minutes.

Answer 1

Displacement of minute hand wrt hour hand in $60min=55min$ space. For hands to co-incide, displacement $=60min$ space.

Time taken $=\frac{60}{55}\times 60=65\frac{5}{11}mins$

But clock coincides every $64min$

Time lost $=65\frac{5}{11}=64=1\frac{5}{11}min$

$\left(in64min\right)$

Time lost in $1$ min $=\frac{16}{11}÷64=\frac{1}{44}min$

Times lost in $24$ hrs. $=\frac{1}{49}\times 60\times 24=32\frac{8}{11}mins$.