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The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much time in a day does the clock gain or lose ?

  1. 440/43 minutes
  2. 450/65 minutes
  3. 5/11 minutes
  4. 65/11 minutes

2 Answers

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In a correct clock:

After 60 min , angle b/w min hand and hour hand is 300.

min hand makes 60 in 1 min. and hour hand makes ½0 in 1 min.

let they meet after t min.

min hand will make a degree t×6 and hour hand will make a degree t×½

So,  t×6 =  t×½ + 300 (already made 300)

solve: t=60/11 min.

total time taken for overtaking 60 + 60/11 = 720/11 min. = 65 and 5/11 min.

So, In the faulty close the hand meet after 65 min.

In 65 min we get 5/11 min extra

In 1 ------------------5/(11×65) min.

in 60 min ---------------- (5×60)/(11×65)min

in 24 hour ---------------- (24× 5× 60 ) / (11×65) min

=$\frac{5\times 60\times 24}{11\times 65} = \frac{1440}{143} min$

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