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(D) Let the initial length of both candles be $L$.The rate of burning for the first candle is $\frac{L}{5}$ per hour,and for the second candle is $\fr

Vedclass · Accepted Answer

$150$

Vedclass · Answer

(D) Let the initial length of both candles be $L$.The rate of burning for the first candle is $\frac{L}{5}$ per hour,and for the second candle is $\frac{L}{3}$ per hour.Let $t$ be the time in hours after which the length of the first candle is $3$ times the length of the second candle.The remaining lengths after time $t$ are $L_1 = L - \frac{L}{5}t$ and $L_2 = L - \frac{L}{3}t$.According to the problem,$L_1 = 3L_2$.Substituting the expressions: $L - \frac{L}{5}t = 3(L - \frac{L}{3}t)$.Dividing by $L$: $1 - \frac{t}{5} = 3 - t$.Rearranging the terms: $t - \frac{t}{5} = 3 - 1$.$\frac{4t}{5} = 2$.$t = \frac{10}{4} = 2.5 \, hr$.Converting to minutes: $2.5 	imes 60 = 150 \, min$.

There are two candles of the same length and size. Both of them burn at a uniform rate. The first one burns in $5 \, hr$ and the second one burns in $3 \, hr$. Both the candles are lit together. After how many minutes is the length of the first candle $3$ times that of the other?

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