How much does a watch gain or lose per day,if | vedclass

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Question

(A) In a correct clock,the hands coincide every $65 \frac{5}{11}$ minutes (or $\frac{720}{11}$ minutes).Given that the hands of the watch coincide eve

Vedclass · Accepted Answer

$32 \frac{8}{11}$ minutes gain

Vedclass · Answer

(A) In a correct clock,the hands coincide every $65 \frac{5}{11}$ minutes (or $\frac{720}{11}$ minutes).Given that the hands of the watch coincide every $M = 64$ minutes.If $M  65 \frac{5}{11}$,the watch loses time.Since $64 The gain per $M$ minutes is $\left(\frac{720}{11} - 64ight)$ minutes.The gain in $24$ hours (or $1440$ minutes) is given by the formula:Gain $= \left(\frac{720}{11} - Might) 	imes \left(\frac{1440}{M}ight)$$= \left(\frac{720 - 704}{11}ight) 	imes \left(\frac{1440}{64}ight)$$= \left(\frac{16}{11}ight) 	imes \left(\frac{1440}{64}ight)$$= \frac{1}{11} 	imes \frac{1440}{4} = \frac{360}{11} = 32 \frac{8}{11}$ minutes.Therefore,the watch gains $32 \frac{8}{11}$ minutes per day.

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

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