Question

Calculate the weight and the percentage of silver in the silver-copper alloy being given that the latters alloy with $3$ kg of pure silver contains 90 per cent of silver and with $2$ kg of $90\%$ silver alloy contains $84$ per cent of silver.

Answer 1

$x:3$

$y:100$

$10:90-y$

$\therefore \frac{90-y}{3}=\frac{10}{x}$----------------------1

$\frac{84-y}{2}=\frac{6}{x}$-------------------2

Dividing Equation 1 & Equation 2, we get

$180-2y=420-5y$

$\Rightarrow 3y=240$

$\Rightarrow y=80$

$\Rightarrow x=\frac{30}{90-80}=\frac{30}{10}=3kg$

Quantity of silver in $x=80\%ofx$

$=0.83ofx=2.4kg$

Weight and percentage of silver$=2.4kg$ or $80\%$