Question

Sterling Silver is $92.5\%$ pure silver. How many grams of Sterling Silver must be mixed to a $90\%$ Silver alloy to obtain a $500$g of a $91\%$ Silver alloy?

• A. $200$ gm
• B. $300$ gm
• C. $400$ gm
• D. $500$ gm

Answer 1

The correct option is A $200$ gm

Let $x$ and $y$ be the weights, in grams, of sterling silver and of the $90\%$ alloy to make the $500$ grams at $91\%.$

$\therefore$ $x+y=500$ ----- ( 1 )

The number of grams of pure silver in $x$ plus the number of grams of pure silver in $y$ is equal to the number of grams of pure silver in the $500$ grams. The pure silver is given in percentage forms.

$\therefore$ $92.5\%ofx+90\%ofy=91\%of500$

Substitute $y$ by $500-x$ from ( 1 ),

$\Rightarrow$ $92.5\%ofx+90\%of(500-x)=91\%of500$

$\Rightarrow$ $\frac{92.5}{100}\times x+\frac{90}{100}(500-x)=\frac{91}{100}\times 500$

$\Rightarrow$ $92.5x+45000-90x=45500$

$\Rightarrow$ $x=200$ grams.

$\Rightarrow$ $200$ grams of Sterling Silver is needed to make the 91% alloy.