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

\frac{2}{7}

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\frac{5}{7}

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\frac{3}{5}

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\frac{4}{5}

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Solution

The correct option is C $\frac{5}{7}$
suppose $L_{1}$ and $L_{2}$ are the length of two different candles.
Suppose rate of burning of Li length candle is $R_{1} = L_{I}$ / (3 hr and 30 minute or 3. 1/2 ) or $L_{1}$ / (7/2) and
rate of burning of L2 length candle is $R_{2} = L_{2} / 5$
Now after 2 hr length become same for both candle means,
$L_{1} - 2 X (R_{1}) = L_{2} - 2 X (R_{2})$ ,
PUT THE VALUE OF $L_{1}$ AND $L_{2}$ in above equation,
$L_{1} - 2 X (2 L_{1} / 7) = L_{2} - 2 X (L_{2} / 5)$
$L_{1} - 4 L_{1} / 7 = L_{2} - 2 L_{2} / 5$
$L_{2} / L_{1} = 5 / 7$
Thus option B is correct answer.

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