Q.16/40 :In a watch the minute-hand and hour hand
coincide after every 65 whole 3/11. How much time does
the watch lose

2 thoughts on “Q.16/40 :In a watch the minute-hand and hour hand<br />coincide after every 65 whole 3/11. How much time does<br />the watch lose”

1. Given : In a watch the minute-hand and hour hand coincide after every 65 whole 3/11.

   To Find : How much time does the watch lose or gain per day?

   Solution:

   In Normal watch

   Hour hand moves x° then minute hand moves (360 + x)° to coincide

   Minute hand 6° in 1 minutes

   Hour hand 0.5° in 1 minutes

   => for 1° of minute hand Hour hand mover 1/12°

   => (360 + x)° minute hand = (360/12 + x/12)° hour hand

   360/12 + x/12 = x

   => 30 = 11x/12

   => x = 360/11

   minute hand moves (360 + 360/11)° = 360 * 12/11 °

   Time in minutes = (360 * 12/11 ) /6 = 720 /11 minutes

   = 1 hr + 60/11 minutes

   = 1 hr + 5 5/11 minutes

   = 65 5/11

   In a watch the minute-hand and hour hand coincide after every 65 whole 3/11.

   => 2/11 minutes advance for every 720 /11 minutes

   => (2/11)/(720/11) = 1/360 minutes advance for every 1 minute

   1 Day = 24 hr = 24 * 60 minutes

   gain in 1 day = 24 * 60 / 360 = 4 minutes

   watch gain per day = 4 Minutes

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2. Step-by-step explanation:

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