Question

A jeweller has bars of 18-carat gold and 12-carat gold.How much of each must be melted together to obtain a bar of 16-carat gold,weighing 120 g?

(Given:Pure gold is 24-carat).

Answer 1

Let x grams of 18 carat gold is added
Thus, the amount of 12 carat gold added is (120 – x) grams.
Purity of gold is 24 carats.
Given that

$x\times \frac{18}{24}+(120–x)\times \frac{12}{24}=120\times \frac{16}{24}$

$\to 18\times x+12(120–x)=120\times 16$

$\to 18\times x+12\times 120–12x=16\times 120$

$\to 6\times x=16\times 120–12\times 120=(16-12)\times 120$

$\to x=\frac{4\times 120}{6}=80$

Thus, 80 grams of 18 carat gold is added with 12carat and 80 carat gold to become 40 grams of 12 carat gold.