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 gm? (Given: Pure gold is 24-carat).

Answer 1

Let x g and y g be the weight of 18-carat and 12- carat gold, respectively.

As per the given condition

`(18x)/24 + (12y)/24 = (120 xx 16)/24`

⇒ 3x + 2y = 320   ...(i)

And

x + y = 120   ...(ii)

Multiplying (ii) by 2 and subtracting from (i), we get

x = 320 – 240

x = 80

Now, putting x = 80 in (ii), we have

80 + y = 120

⇒ y = 40

Hence, the required weight of 18-carat and 12-carat gold bars are 80 g and 40 g, respectively.