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).
Let the weight of 18 - carat gold be x g.
∴ weight of 12 - carat gold = (120 - x) g
24 - carat equals 100% gold (Given)
∴ % of gold in 18 - carat gold = (100/24) × 18 = 75%
and % of gold in 12 - carat gold = 50%
and % of gold in 16 - carat gold = (200/3)%
Now,
75% of x + 50% of (120 - x) = (200/3)% of 120
⇒ x + 240 = 320
⇒ x = 80
Thus, the weight of 18 - carat gold = 80 g and the weight of 12 - carat gold = 40 g.