Question

How much does a watch lose per day, if it's hands coincide every 64 minutes?​

Answer 1

Answer:

It will lose 360/11 minutes in 24 hours

Step-by-step explanation:

In a correct clock, in 60 minutes, minute hand gains 55 minute spaces over the hour hand.

NOTE: FIGURES IN ITALICS DENOTE MIXED FRACTIONS

∴ In a correct clock, time taken for the minute hand to gain 60 minute spaces over the hour hand = 60×60/55=720/11=65(5/11) minutes

Now, in the given watch, hands coincide every 64 minutes.

or in the given watch, in 64 minutes, minute hand gains 60 minute spaces over the hour hand.

∴Loss in 64 minutes =720/11 -64 = 16/11 minutes

∴Loss in 1 minute =16/(11×64)

Now 24 hours = 24×60 minutes=1440 minutes

∴Loss in 1440 minutes =16×1440/(11×64)

=360/11 minutes

=32(8/11) minutes