Two candles of equal height but different thickness are lighted. The first burns off in 6 hours and the second in 8 hours. How long, after lighting both, will the first candle be half the height of the second?

Given that, the first candle burns off in

6

hrs, the

\frac{1}{6}

part of the candle burns in 1 hr. As the second candle burns off in

8

hrs, the

\frac{1}{8}

part of the candle burns in 1 hr.
Let

L

be the length of the candles.
Considering

t

as the time taken by the first candle to be half of the length of the second candle.
Then, the first candle burns

\frac{Lt}{6}

part in

t

hrs and the second candle burns

\frac{Lt}{8}

part in

t

hrs. Hence,

(L - \frac{Lt}{6}) = \frac{1}{2} (L - \frac{Lt}{8})

\Rightarrow L (1 - \frac{t}{6}) = \frac{L}{2} (1 - \frac{t}{8})

\Rightarrow \frac{6 - t}{6} = \frac{8 - t}{16}

\Rightarrow \frac{6 - t}{3} = \frac{8 - t}{8}

\Rightarrow 8 (6 - t) = 3 (8 - t)

\Rightarrow 48 - 8 t = 24 - 3 t

\Rightarrow 5 t = 24

\Rightarrow t = \frac{24}{5}

Therefore, the time taken by the first candle to be half of the length of the second candle is

\frac{24}{5}

.
Hence the correct option is 1.

Two candles of equal height but different thickness are lighted. The first burns off in $6$ hours and the second in $8$ hours. How long, after lighting both, will the first candle be half the height of the second?