Question of The Day01-10-2020

At what time minute hand will be ahead of hour hand by 2\({2 \over 3}\) minutes between 9 AM to 10 AM?


Correct Answer : a ) 9:52 AM

Explanation :

As, minute hand can cover 3600 in 60 minutes

So, speed of minute hand will be=\({360 \over 60}\)=6/min

As, hour hand can cover 3600 in 12 hours

So, speed of hour hand will be=\({360 \over 12×60}\)=\({1 \over 2}\)/min

Now, Relative speed of minute and hour hand=6-\({1 \over 2}\)=\({11^0 \over 2}\) /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=\({270 \over {11 \over 2}}\)=\({540 \over 11}\) minutes….. 1

Now, according to the question minute hand has to be 2\({2 \over 3}\)minutes ahead of hour hand

As, in 60 minutes, minute hand covers 3600

So, in 1 minute, minute hand will cover 60

Thus, in 2\({2 \over 3}\) minutes, minute hand will cover=\({8 \over 3}\)×6=160

Now, to cover 200 distance minute hand, moving relative with the hour hand will take the time equal to

⇒time=\({16 \over {11 \over 2}}\)=\({32 \over 11}\)minutes…. 2

Adding 1 and 2 we will get the required time

⇒Required time=\({540 \over 11}+{32 \over 11}={572 \over 11}\)=52 minutes

So, after exact 9:00 AM, minute hand will take 52 minutes to get ahead of hour hand by 2\({2 \over 3}\) 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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