GATE | GATE-CS-2014-(Set-2) | Question 65

At what time between 6 a.m. and 7 a.m. will the minute hand and hour hand of a clock make an angle closest to 60o
(A) 6:22 am
(B) 6:27 am
(C) 6:38 am
(D) 6:45 am


Answer: (A)

Explanation:

Speed of the Hour hand = ( 360 degree ) / ( 12 * 60 minutes ) 
                       = 0.5 degree / minute.
Speed of the minute hand = ( 360 degree ) / ( 60 minutes ) 
                         = 6 degree / minute.

At 6 am, hour hand will point vertically downward to 6 in the clock, and minute hand will point vertically upward to 12 in the clock. ( Hence they are opposite with a gap of 180 degree between them).

Now after t minutes , The angle between these two hands will be either of the below two:


(180 - 6t) + 0.5t, when the minute hand is 
                   behind the hour hand or,

6t - (180 + 0.5t), when the minute hand is 
                    ahead of hour hand,

Now the the question asks for angle of 60 degree.

Hence, 
(180 - 6t) + 0.5t = 60 , we get t = 21.8 minute
and
6t - ( 180 + 0.5t ) = 60, we get t = 48 minutess

Hence the closest to answer is 22 minutes, i.e. 6.22 am. Hence answer is A.


Quiz of this Question



My Personal Notes arrow_drop_up