Question

How many minutes will a watch lose per day, if its hands coincide every 64 minutes?

• A. 36 7/9 min
• B. 32 8/11 min
• C. 34 3/11 min
• D. 65 5/11 min

Answer 1

The correct option is B 32 8/11 min

Since the minute hand gains 5.5 degrees every minute, originally it will take the minute hand $\frac{360}{5.5}=65\frac{5}{11}$ minutes.
But here it only takes 64 minutes for them to meet again.
So, the watch is actually gaining $65\frac{5}{11}-64=\frac{16}{11}$ minutes every 64 minutes
So, in a day = $\frac{\frac{16}{11}}{64}\times 60\times 24=\frac{360}{11}$ minutes = $32\frac{8}{11}$ minutes