Legend has it that this question stumped all but 5 students in a school when it first appeared in an exam paper a few years back.

Question:

Two candles, one of which is one cm longer than the other, are lit. The longer one is lit at 4:30pm and the shorter one at 6:00 pm. At 8:30 they are both the same length. The longer one burns out at 10:30pm and the shorter one at 10:00pm. How long was each candle originally?

Solution:

Time taken for L (longer candle) = 6 hrs (4:30 to 10:30pm)

Time for S (shorter candle) = 4 hrs (6 to 10pm)

At 8:30 they are at the same length.

Time taken for L to burn out –> 2 hours   ===> Candle is 2/6 or 1/3 long

Time taken for S to burn out –> 1.5 hours  ===> Candle is 1.5/4 or 3/8 long

Since the 2 lengths are the same at 8:30, this means that 1/3 of L is the same as 3/8 of S

or 3/9 of L is the same as 3/8 of S

so ratio  of L to S is 9:8

L is longer by one unit. We are told L is longer by 1 cm, so L is 9cm and S 8 cm long.