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 or gain per day?
Answers
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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