If the hands of a clock coincide every 65 min | vedclass

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Question

(A) In a correct clock,the minute hand and hour hand coincide every $65 \frac{5}{11}$ minutes.Given that the clock in question coincides every $65$ mi

Vedclass · Accepted Answer

$10 \frac{10}{143}$

Vedclass · Answer

(A) In a correct clock,the minute hand and hour hand coincide every $65 \frac{5}{11}$ minutes.Given that the clock in question coincides every $65$ minutes,it is a fast clock.The gain in $65$ minutes is $65 \frac{5}{11} - 65 = \frac{5}{11}$ minutes.Therefore,the gain in $1$ minute is $\frac{5/11}{65} = \frac{5}{11 	imes 65} = \frac{1}{11 	imes 13} = \frac{1}{143}$ minutes.In $24$ hours,there are $24 	imes 60 = 1440$ minutes.Total gain in $24$ hours $= 1440 	imes \frac{1}{143} = \frac{1440}{143} = 10 \frac{10}{143}$ minutes.

If the hands of a clock coincide every $65$ minutes (true time),how many minutes will the clock gain in $24$ hours?

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