Question

In two alloys copper and zinc are related as $4:1$ and $1:3$. After alloying together $10$ kg of the first alloy, $16$ kg of the second and several kg of pure copper, an alloy was obtained in the ratio of copper to zinc was $3:2$. Find the weight of the new alloy.

Answer 1

Copper $1^{st}$ Alloy of $10kg$ $=\frac{4}{5}\times 10=8kg$

Zinc in $1^{st}$ Alloy of $10kg$ $=2kg$

Copper in $2^{nd}$ Alloy of $16kg$ $=\frac{1}{4}\times 16=4kg$

Zinc in $2^{nd}$ Alloy of $16kg$ $=\frac{3}{4}\times 16=12kg$

Total Copper $=12kg$

Total Zinc $=14kg$

In the new alloy $xkg$ of copper was added

$\therefore$ Total copper in new alloy $=12+x$

$\therefore$ New alloy copper to zinc ratio

$\frac{12+x}{14}=\frac{3}{2}$

$24+2x=42$

$2x=18$

$x=9kg$

$\therefore$ $10kg$ of first alloy

$16kg$ second alloy

$\underset{–}{9kgof}$ copper

$\underset{–}{35kgof}$ New Alloy