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?
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Meera studied for 3 hours in candle light.
Assume that the initial length of both the candle was L and Meera studied for X hours.
In X hours, total thick candle burnt = XL/6
In X hours, total thin candle burnt = XL/3
After X hours, total thick candle remaining = L – XL/6
After X hours, total thin candle remaining = L – XL/3
Also, it is given that the thick candle was twice as long as the thin one when she finally went to sleep.
(L – XL/6) = 2(L – XL/3)
(6L – XL)/6 = 2(3L – XL)/3
(6 – X)/6 = 2L(3 – X)/3
18 – 3X =12(3 –X)
18 – 3X = 36 – 12X
18 = 9X
X = 2
Hence, Meera studied for 2 hours i.e. 60 minutes in candle light
Lets assume length of both candle is 18cm(6×3)
So thicker candle burns 3 cm per hour
& thinner candle burns 6 cm per hour.
After one hour thicker candle will be 15 cm & thinner will be 12 cm.
After two hours thicker candle will be 12 cm & thinner will be 6 cm.
Hence the answer!