Question

Brass is an alloy of copper and zinc; bronze is an alloy containing $80$ per cent of copper, $4$ of zinc, and $16$ of tin. A fused mass of brass and brozen is found to contain 74 per cent. of copper, 16 of zinc, and $10$ of tin : find the ratio of copper to zinc in the composition of brass.

Answer 1

Let the proportion of Copper and Zinc in Brass be $x:y$

Also, let the amount of brass and bronze in the fused mass is $m$ and $n$ respectively

Percentage of Tin in the fused mass $=m\times 0+n\times 16=(m+n)\times 10⟹10m=6n⟹\frac{m}{n}=\frac{3}{5}$

Percentage of Zinc in the fused mass $=m\times y+n\times 4=(m+n)\times 16⟹(y-16)m=12n⟹\frac{12}{y-16}=\frac{m}{n}=\frac{3}{5}$

$⟹3y-48=60⟹y=36$

Also, $x+y=100⟹x=64$

Therefore Ratio of Copper and Zinc in Brass is $64:36$