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 candle's height was the shot 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 B $\frac{5}{7}$
Let lengths are $l_{1}$ and $l_{2}$ and thickness are $x_{1}$ and $x_{2}$ .
$l_{1} \equiv 3.5 h r$ and $l_{2} \equiv 5 h r$ .
$l_{1} - 2 (\frac{l_{1}}{3.5}) = l_{2} - 2 (\frac{l_{2}}{5})$
$\frac{3.5 l_{1} - 2 l_{1}}{3.5} = \frac{5 l_{2} - 2 l_{2}}{5}$
$\frac{1.5 l_{1}}{3.5} = \frac{3 l_{2}}{5}$
$\frac{l_{1}}{l_{2}} = \frac{3.5 \times 3}{1.5 \times 3} \Rightarrow \frac{7}{5}$ or $\frac{l_{2}}{l_{1}} = \frac{5}{7}$ .
Hence, option B is correct.

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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 candle's height was the shot candle initially?

The correct option is B 57Let lengths are l1 and l2 and thickness are x1 and x2.l1≡3.5 hr and l2≡5 hr.l1−2(l13.5)=l2−2(l25)3.5l1−2l13.5=5l2−2l251.5l13.5=3l25l1l2=3.5×31.5×3⇒75 or l2l1=57.Hence, option B is correct.

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 candle's height was the shot candle initially?