Question

The minute hand of a clock overtakes the hour hand at the interval of 65minutes.How much in a day does the clock gains or lose

Answer 1

Hi there!
Here's the answer:

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•••• Points to Remember : ••••

¶¶¶ Overtaking Interval in a Correct clock:

In Correct Clock, the minute hand gains 55 spaces over the hour hand in 60 minutes.

In every hour, both the hands coincide once.

To be together again, the minute hand must gain 60 min. over the hour hand.

55 min. are gained in 60 min.
60 min. are gained in [(60/55)×60] = 720/11 = 65 5/11 min.

•°• Hands of clock are together for every 65 5/11 min.
i.e., Overtaking Interval "O" = 65 5/11 min.
=> O = 65 5/11

¶¶¶ To find whether it is gain/loss
If x < O, the clock is gaining.
If x > O, the clock is losing.

¶¶¶ Gain/Loss in x min =
= | (Overtaking Interval) - x | min.
= | O - x | min

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Now ,

Given x = 65

65< 65 5/11
•°• It is a gaining clock.

Gain in 65 min= [O - 65] min.
= [65 5/11] - 65
= 5/11 min

Gain in 24 hours = [(24×60×5)/(11×65)]
= 1440/143
= 10 10/143

•°• In a day, Clock gains 10 10/143 minutes

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Hope it helps