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

90

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120

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135

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150

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Solution

The correct option is D $150$
Let $x$ be the length of each candle.
After time $^{'} t^{'}$ , the length of the candles are $x - \frac{x}{5} t$ and $x - \frac{x}{3} t$ .
According to the question,
$(x - \frac{x}{5} t) = 3 (x - \frac{x}{3} t) \Rightarrow 1 - \frac{t}{5} = 3 - t \Rightarrow t = 2.5 hrs = 150 min$

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

The correct option is D 150 Let x be the length of each candle. After time ′t′, the length of the candles are x−x5t and x−x3t. According to the question, (x−x5t)=3(x−x3t)⇒1−t5=3−t⇒t=2.5 hrs=150 min

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