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).

Question

Philoid · Accepted Answer

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.