At what time minute hand will be ahead of hour hand by 2 minutes between 9 AM to 10 AM?
Answer
Correct Answer : a ) 9:52 AM
Explanation :As, minute hand can cover 3600 in 60 minutes
So, speed of minute hand will be==60 /min
As, hour hand can cover 3600 in 12 hours
So, speed of hour hand will be==0 /min
Now, Relative speed of minute and hour hand=6-= /min
When minute hand was at 12’o clock mark and hour hand is at 9 AM, then in clockwise direction rotational distance between minute and hour hand will be = 300 × 9 = 2700
Now, time taken by minute hand, moving relatively with the hour hand to cover 2700 distance will be
⇒Time== minutes….. 1
Now, according to the question minute hand has to be 2minutes ahead of hour hand
As, in 60 minutes, minute hand covers 3600
So, in 1 minute, minute hand will cover 60
Thus, in 2 minutes, minute hand will cover=×6=160
Now, to cover 200 distance minute hand, moving relative with the hour hand will take the time equal to
⇒time==minutes…. 2
Adding 1 and 2 we will get the required time
⇒Required time==52 minutes
So, after exact 9:00 AM, minute hand will take 52 minutes to get ahead of hour hand by 2 minutes between 9 AM to 10 AM
Thus, the time at which this happens will be 9:52 AM.
Hence, (a) is the correct answer.
Such type of question is asked in various government exams like RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA, UP SI etc.
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