Answer

Correct Answer : a ) 9:52 AM

As, minute hand can cover 360⁰ in 60 minutes

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

As, hour hand can cover 360⁰ in 12 hours

So, speed of hour hand will be=\({360 \over 12×60}\)=\({1 \over 2}\)⁰ /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.

Read Daily Current Affairs, Banking Awareness, Hindi Current Affairs, Word of the Day, and attempt free mock tests at PendulumEdu and boost your preparation for the actual exam.