Question

An alloy contains zinc, copper and tin in the ratio $2:3:1$ and another alloy contains copper, tin and lead in the ratio $5:4:3.$ If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in new alloy will be

• A. $\frac{1}{8}$ kg
• B. $\frac{1}{6}$ kg
• C. $\frac{7}{9}$ kg
• D. $\frac{1}{2}$ kg

Answer 1

The correct option is A $\frac{1}{8}$ kg

In first alloy, ratio of zinc $\left(Z\right)$, copper $\left(C\right)$ and tin $\left(T\right)$ is given as,
$Z:C:T=2:3:1$
Now, let the weight of first alloy be $12$ kg (taken as $4$ kg zinc, $6$ kg copper and $2$ kg tin)

In second alloy, ratio of copper $\left(C\right)$, tin $\left(T\right)$ and lead $\left(L\right)$ is given as,
$C:T:L=5:4:3$
Now, let the weight of second alloy be $12$ kg (taken as $5$ kg copper, $4$ kg tin and $3$ kg lead)

Alloys are mixed together to form third alloy. Then the ratio of content in it,
$Z:C:T:L=4:(6+5):(2+4):3$
Weight of third alloy $=12+12=24$ kg
So, weight of lead $=\frac{3}{24}=\frac{1}{8}$ kg