The Candle Light Studying Hours
What was the question?
It's clear that, the thick candle lasts for 4 hours and thin one lasts only 3 hours.
If L is length of these candles (they are of equal length) then thick candle burns L/4 per hour and thin one burns L/3 per hour.
Let's assume Vipul studied for X hours.
In X hours, amount of thick candle burnt = XL/4
In X hours, amount of thin candle burnt = XL/3
After X hours, amount of thick candle remaining = L - XL/4
After X hours, amount of thin candle remaining = L - XL/3
Also, it is given that the thick candle was twice as long as the thin one when he finally went to sleep.
(L - XL/4) = 2(L - XL/3 )
L(1 - X/4) = 2L (1 - X/3)
(1 - X/4) = 2(1 - X/3)
3(4 - X) = 8(3 - X)
12 - 3X = 24 - 8X
5X = 12
X=12/5
Converting 12/5 hours into minutes as X = 12/5 * 60 = 144 minutes.
Hence, Vipul must have studied for 2 hours and 24 minutes.
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