' $n$ ' litres of oil was poured into a tank and it was still $e %$ empty. How much oil must be poured into the tank in order to fill it to the brim?

\frac{n e}{100 + e}

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\frac{100 - e}{n e}

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\frac{n e}{100 - e}

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\frac{100 + e}{n e}

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Solution

The correct option is D $\frac{n e}{100 - e}$
Given $n$ litres of oil poured into the tank and
the amount space still empty is $e %$
Let capacity of bank $= C$ litres then
amount of space still empty $= e %$ of $C$
$= \frac{e}{100} + C$
Since, capacity of tank $=$ filled space $+$ empty space.
$\Rightarrow C = n + \frac{e}{100} \times C$
$\Rightarrow C - \frac{e C}{100} = n$
$\Rightarrow C (1 - \frac{e}{100}) = n$
$∴ C = \frac{n \times 100}{100 - e}$
Suppose $x$ L is to be poured to fill the tank completely.
So, $x =$ total capacity of tank $-$ amount of oil filled.
$\Rightarrow x = C - n$
$= \frac{100 n}{100 - e} - n$
$= \frac{100 n - 100 n + n e}{100 - e}$
$∴ x = \frac{n e}{100 - e}$

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