CANDLE PROBLEM

Two candles of the same height are lighted at the same time. The first is consumed in 8 hours and the second in 6 hours. Assuming that each candle burns at a constant rate, in how many hours after being lighted was the first candle twice the height of the second? (i.e., the ratio between the first and second candles becomes 2 : 1)

SOLUTION: 

Let the candles be A and B with height 24 meters each (LCM of 8 and 6)

                                                       A          B

    Completely Burns in         8 hr     6 hr

     in 1 hr Candle burns by         3           4   (Divide height by time)

        After burning for time, T, 

        Heights reduced by                  3T             4T

        Remaining Height is            24 - 3T        24 - 4T

    It is Given that, The ratio of heights will be 2 : 1, on applying this

                                                (24 - 3T) : (24 - 4T) = 2 : 1

    On solving for T, we will get T = 24/5 = 4 hours 48 mins.

    So, after 4 hr 48 mins of lighting, the candles height will be in the ratio of 2:1.