To x litres of an x% solution of acid, y litres of water is added to get (x-10)% solution of acid. If x > 20, then value of y is

\frac{x^{2}}{100}

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\frac{10 x}{x - 10}

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\frac{10 x}{x + 10}

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\frac{10 x^{2}}{x - 10}

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None of the above

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Solution

The correct option is B $\frac{10 x}{x - 10}$

Here, quantity of acid in x litre of solution
$= 4 \times \frac{x}{100} = \frac{x^{2}}{100}$
Quantity of water =y
$∴ \frac{\frac{x^{2}}{100}}{x + y} \times 100 = x - 10$
or $\frac{x^{2}}{x + y} = x - 10$
or $x^{2} = x^{2} - 10 x + y (x - 10)$
or $y = \frac{10 x}{x - 10}$
As x > 20

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To x litres of an x% solution of acid, y litres of water is added to get (x-10)% solution of acid. If x > 20, then value of y is

The correct option is B 10xx−10 Here, quantity of acid in x litre of solution =4×x100=x2100 Quantity of water =y ∴x2100x+y×100=x−10 or x2x+y=x−10 or x2=x2−10x+y(x−10) or y=10xx−10 As x > 20