Ramesh and Rahul were making joint-study for their semister examinations and the lights went off. It was around 10.00 pm .They lighted two uniform candles of equal length. The First candle is supposed to last six hours and the second one two hours less. When they finally went to sleep, the first candle was thrice as long as the second one. Approximately at what time did they go to sleep?
Assume that the initial length of both the candle was L and they studied for P hours.
here the first candle would be burnt 6 hours. Therefore in 1 hour L/6th of the candle would be burnt. Similarly in P hours, PL/6 th of the candle would be burnt.Similarly second candle, length of that candle burnt in P hours = PL/4
After P hours, total 1st candle remaining = L - PL/6
After P hours, total 2nd candle remaining = L - PL/4
Here the First candle was thrice as long as the second one when they finally went to sleep.
(L - PL/6) = 3(L - PL/4)
solve the above one we get
24 - 4P = 72 - 18P
P = 3.4.So here 3 hours and 24 minutes Here 4 hours = 4/10 x 60 = 24 minutes
So they slept 3 hours and 24 minutes after 10.00 p.m i.e. at 1.24 am.
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