Question

$50$kg of an alloy of lead and tin contains $60\%$ lead. How much lead must be melted into it to make an alloy containing $75\%$ lead ?

Answer 1

Quantity of lead in $50$ kg of alloy $=60\%$ of $50$ kg $=\frac{60}{100}\times 50$kg $=30$ kg.

Let the required quantity of lead to be added be $x$ kg.

Then, weight of lead $=(30+x)$ kg.

And, weight of new alloy $=(50+x)$ kg.

Percentage of lead in new alloy $=(\frac{30+x}{50+x}\times 100)\%$

According to the question,

$\Rightarrow \left(\frac{30+x}{50+x}\right)\times 100=75$

$\Rightarrow \left(\frac{30+x}{50+x}\right)=\frac{75}{100}$

$\Rightarrow \left(\frac{30+x}{50+x}\right)=\frac{3}{4}$

$\Rightarrow 4(30+x)=3(50+x)$

$\Rightarrow 120+4x=150+3x$

$\Rightarrow 4x-3x=150-120$

$\Rightarrow x=30$

$\therefore$ Quantity of lead to be added $=30$ kg