Question

Two candles of equal length start 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. $2\frac{1}{2}$ hours
• B. $3\frac{1}{2}$ hours
• C. $3\frac{1}{9}$ hours
• D. $3\frac{1}{3}$ hours

Answer 1

The correct option is D

$3\frac{1}{3}$ hours

Step 1: Use the given information to get the desired result.

It is given that two candles of equal length start burning at the same instant.

Let $x$ be the length of both candles

The first candle burns in 5 hrs.

The speed of melting of candle 1 is $\frac{x}{5}$.

Also, the second candle burns in 4 hrs.

The speed of melting of candle 2 is $\frac{x}{4}$.

At any time $t$, the length of candle 1 is $\left(x-\frac{xt}{5}\right)=x\left(1-\frac{t}{5}\right)$.

At any time $t$, the length of candle 2 is $\left(x-\frac{xt}{4}\right)=x\left(1-\frac{t}{4}\right)$.

Now, one candle is 2 times the length of the other.

$\begin{array}{rcl}& \Rightarrow & x\left(1-\frac{t}{5}\right)=2x\left(1-\frac{t}{4}\right)\\ & \Rightarrow & 1-\frac{t}{5}=2-\frac{t}{2}\\ & \Rightarrow & \frac{5t-2t}{10}=1\\ & \Rightarrow & t=\frac{10}{3}\\ & \Rightarrow & t=3\frac{1}{3}\text{hours}\end{array}$

Thus, option (d) is correct.