Question

Two candles of equal length starts burning at the same instant. One of the candles burns in 5 hrs and the other in 4 hrs. By the time one candle is 2 times the length of the other, the candles have already burnt for

• A. $2\frac{1}{2}hrs$
• B. $3\frac{1}{2}hrs$
• C. $3\frac{1}{9}hrs$
• D. $3\frac{1}{3}hrs$

Answer 1

The correct option is D $3\frac{1}{3}hrs$

Let the length of both the candles be L.
Then, speed of melting of candle 1 = $\frac{L}{5}$
speed of melting of candle 2 = $\frac{L}{4}$
At any time, t, the length of candle 1 = $L(1-\frac{t}{5})$
length of candle 2 = $L(1-\frac{t}{4})$
Thus, $L(1-\frac{t}{5})=2L(1-\frac{t}{4})$
$1-\frac{t}{5}=2-\frac{t}{2}$
$\frac{5t-2t}{10}=1$
$t=\frac{10}{3}=3\frac{1}{3}$ hrs.