Q32 / 58 · KVPY 2016 (SA) · Mathematics
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?
- A90
- B120
- C135
- Correct answerD150
Solution
Let $\mathrm{V}_{1} \& \mathrm{~V}_{2}$ are rates of burning for both candles respectively $\& \mathrm{~L}$ is the length of each candle
$\mathrm{V}_{1}=\frac{\mathrm{L}}{5} \quad \mathrm{~V}_{2}=\frac{\mathrm{L}}{3}$
Let after time 't', their lengths are $\ell_{1} \& \ell_{2}$
$\begin{array}{l}
\ell_{1}=\mathrm{L}-\frac{\mathrm{L}}{5} \mathrm{t} \\
\ell_{2}=\mathrm{L}-\frac{\mathrm{L}}{3} \mathrm{t} \\
\& \ell_{1}=3 \ell_{2} \text { (Given) } \\
\Rightarrow \mathrm{L}-\frac{\mathrm{L}}{5} \mathrm{t}=\left(\mathrm{L}-\frac{\mathrm{L}}{3} \mathrm{t}\right) 3 \\
\Rightarrow \frac{5-\mathrm{t}}{5}=3-\mathrm{t} \\
\Rightarrow 5-\mathrm{t}=15-5 \mathrm{t} \\
\Rightarrow 4 \mathrm{t}=10 \Rightarrow \mathrm{t}=2.5 \mathrm{hrs}=150 \mathrm{~min}
\end{array}$
Hence, the correct answer is option: 'D'.