clock

Question

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

A)$32\frac{8}{11}$ min

B)$36\frac{5}{11}$ min

C)90 min

D)96 min

Answer 1

Ideal speed of minute hand = 60 minute distance per hr

Ideal speed of hour hand = 5 minute distance per hr

So, ideally collision happens when

$60 \times x = 5 \times x + 60$

i.e., the minute hand completes one full revolution extra to the hour hand.

Solving, $x = \frac{12}{11}\; hr = \frac{720}{11}$ minutes $=65\frac{5}{11}$ minutes.

Given collision time of the clock = 64 minutes.

So, clock is losing $1 \frac{5}{11}$ minutes every $64$ minutes.

So, minutes lost in a day ($60 \times 24$ minutes)

$ = 1 \frac{5}{11} \times \frac{60 \times 24}{64}

\\= \frac{16}{11} \times \frac{15 \times 24}{16}

\\= \frac{360}{11}  = 32 \frac{8}{11}.$