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A wall clock and a Table clock are set to correct time today on 10 pm. Wall clock looses 3 minute in 1st hour, 6 minutes in the second hour and 9 minutes in the third hour and so on. Table clock looses 5 minutes in the 1st hour, 10 minutes in the second hour and 15 minutes in the third hour and so on. When will they show the same time?

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they will show the same time when the time difference between them is 12hours( Why 12 hours? you can get it from the question as we have 12 hours in a table clock and wall clock )

taking the difference from both clock:--

=>2 + 4+ 6 +8..................= 12 * 60 mins 

(as one clock looses 3,6,9....... and other 5,10,15...............)

=>2(1+2+3+................k) = 720

=>2(k(k+1)/2)=720

=>k2+k-720=0 (solving eqn we get)

=> k= 26.3374738 hours answer

so after 26.3374 hours it will show the same time.

which means 10pm + 26.3374738 hrs = 10pm +24+ 2.3374738 hr

=10pm+2hr + .3374738 hr(.33774738*60 min)

=12pm + 20 min + .24842804 min( .24842804*60 sec)

=12:20:14:9056823 sec.

so it shows corect timing at 12:20:14:9056823 answer.. :p

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