The Candle Light Study

Power went off when Vipul was studying. It was around 2:00 AM. He lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last four hours and the thin one one hours less. When he finally went to sleep, the thick candle was twice as long as the thin one.

For how long did Vipul study in candle light?

Well, he studied in candle light for....hours. Know here! 

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)

 

(4 - X)/4 = 2(3 - 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.