How many times are the hour hand and the minute hand of a clock of a right angles during their motion from 1 : 00 pm to 10 : 00 pm ?
A. 9
B. 10
C. 18
D. 20
Answer: Option C
Solution(By Examveda Team)
The duration from 1 : 00 pm to 10 : 00 pm is 9 hours and during each of these 9 hours the hands of the clock are at right angles twice.So, required number = 9 × 2 = 18
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The option given here seems to be wrong,it should be 16 times,because we know that in 9 hours,the minute hand makes 360x9 =3240 degree and hour hand also makes 30x9=270 degree .Therefore,the relative angle is 3240-270=2970 degree.Required number of times=2970/180=16.5 ie,16 times,First right angle is at the time 1:21.8181...PM,then after each 32.7878... minutes there will be right angles.the last right angle is at 9:32.7272...PM.So there will be 16 right angles at times {1:21.8181PM, 1:54.5454PM, 2:27.2727PM, 3:00PM, 3:32.7272PM, 4:05.4545PM, 4:38.1818PM, 5:10.9090PM, 5:43.6363PM, 6:16.3636PM, 6:49.0909PM, 7:21.8181PM, 7:54.5454PM, 8:27.2727PM, 9:00PM and 9:32.7272PM}