+1 vote
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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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0
Here relative speed also increases every hour
+1
What is the answer?

I am getting it as 12:20 AM.

## 1 Answer

+2 votes
Best answer

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

by Boss (12.2k points)
selected
0
@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 :)
+1
@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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