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

Answer: Option A

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