# At what time does it happens puzzle

Sometime during every hour the minute hand lies directly above the hour hand.

At what time between 4 and 5 o’clock does this happen?

**Answer** – 04 : 21 : 48.9942

Let’s start with 12.00 o clock… Both hands overlap…

Let an hour pass….. Min hand will point to 12 again…. But in the mean time, hours hand would move to 1 (from 12 to 1)….

So min hand must move from 12 to 1 ( it takes 5 min or 300 seconds)

But hours hand also over in that time. It moves by

300 * 0.0083 = 2.5 degrees

To cover up that 2.5 degrees, min Hand takes 2.5/0.1 = 25 seconds…

But in that 25 seconds, hour hands move by 25 * 0.0083 = 0.2075 degrees…

To cover up that 0.2 degrees it takes 2.075 degrees…..

And keep continuing thus was….

Total approx time is 25 +2.075. ,0.17+0.00141+0.00117+0.00097 = 27.24855 seconds

Every 65 min 27.24855 seconds once they overlap…..

Let’s continue… After an hour(60 min) , min hand would be at 1 and hour hand would have moved to 2 … So five more min to compensate it…

At 2.10 they over lap again….

So every 65 min 27.24855 seconds once they over lap….

So let’s calculate…

12 : 00 : 00

01 : 05 : 27.24855

02 : 10 : 54.7971

03 : 16 : 21.74565

04 : 21 : 48.9942

05 : 27 : 16.24275

So the answer is 04 : 21 : 48.9942

240/11 minutes after 4 o clock

i answered first

### Your Answer

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