# Clock Aptitude Question

1 vote
439 views
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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Here relative speed also increases every hour
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I am getting it as 12:20 AM.

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)

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

selected
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@balaji jegan : if u can read the question once clearly and see the solution accordingly u will get to know everything! difference after second hour is 2+4 = 6 and in the solution its (2+4)+6+8....................... and you have missed out on something that it has clearly mentioned about clock loses every hour and accordingly we have to solve the question.
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@arvin , nice solution. Thank you for the answer.. :)
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@ankit thanks bro :)
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@arvin, 10PM+26.3374... is 10PM+1day+2hours+ .3375 hours (is 20.25 minutes) (.25 minutes is 15 seconds)

=  12:20:15 AM on the second day
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yes to be more precise its 12:20:14:90 :p  i think.

thanks as i forgot to correct the timing.

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