Question

Two candles are of different lengths and thicknesses. The short and the long ones can burn respectively for $3.5$ hour and $5$ hours. After burning for $2$ hour, the lengths of the candles become equal in length. What fraction of the long candles height was the short candle initially ?

• A. $\frac{2}{7}$
• B. $\frac{5}{7}$
• C. $\frac{3}{5}$
• D. $\frac{4}{5}$

Answer 1

The correct option is B $\frac{5}{7}$

Let length are $l_1$ and $l_2$ and thickness are $x_1$ and $x_2$.
$l_1=3.5$ hr and $l_2=5$ hrs.
$l_1-2\left(\frac{l}{3.5}\right)=l_2-2\left(\frac{l_2}{5}\right)$
$\frac{3.5l_{-}2l_1}{5l_2-2l_1}=\frac{5l_2-2l_2}{5}$
$\frac{1.5l_1}{3.5}=\frac{3l_2}{5}$
$\frac{l_1}{l_2}=\frac{3.5\times 3}{1.5\times 5}\Rightarrow \frac{7}{5}$ or $\frac{l_2}{l_1}=\frac{5}{7}$