Meera was studying for her examinations and the lights went off. It was around 2:00 AM. She lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last six hours and the thin one three hours. When she finally went to sleep, the thick candle was twice as long as the thin one. For how long did Meera study in candle light?

• Let x be the length of Thinner candle left
  Therefore thicker candle is left 2x
  Now,
  Since both the candles were burnt for the same time so;
  The rate of burning of both candles are
  Thinner= 3/l (In 3 hours l length candle is totally burnt)
  Thicker= 6/l (In 6 hours l length candle is totally burnt)
  now equating
  (3/l)*(l-x)=(6/l)*(l-2x)
  this implies
  x=l/3
  So we have been left with l/3 lenth of thinner candle wich implies the candle had been burninh for two hour
  
  So answer is 4 A.M.
  
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• At any time 't':
  Length of thinner candle(x): L(1-t/3)
  Length of thicker candle(y): L(1-t/6)
  
  given condition y=2x => t=2hrs.
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• till 4 a.m....
  
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• it will be 5.00 am because after 3 hr thiner candle burnd and hiker candle becam half..
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