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$50$ $g$ of an alloy of gold and silver contains $80$ $%$ gold(by weight). The quantity of gold, that is to be mixed up with this alloy, so that it may contain $95$ $%$ gold, is:

A

$200$ $g$

B

$150$ $g$

C

$50$ $g$

D

$10$ $g$

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Solution

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Correct option is B)

$50 g$ of gold contains $80$ % of gold.

Hence amount of gold $= \frac{8 0}{1 0 0} \times 50 = \frac{8 0}{2} = 40 g$

So, $\frac{4 0 + x}{5 0 + x} = \frac{9 5}{1 0 0} = \frac{1 9}{2 0}$

$20 (40 + x) = 19 (50 + x)$

$800 + 20 x = 950 + 19 x$

$20 x - 19 x = 950 - 800$

$x = 150 g$

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