Question

A jeweller has bars of 18 carat gold and 11 carat gold . How much of each must be melted together to obtain a bar of 16 carat gold weighing 120 grams A jeweller has bars of 18 carat gold and 11 carat gold . How much of each must be melted together to obtain a bar of 16 carat gold weighing 120 grams

Answer 1

Hi ,Sreyamarium very good morning to u hope this will help u

A jeweler has bars of 18 carat gold and 12 carat gold.

melted together to obtain a bar of 16 carat gold, weighing 120 gm

Given pure gold is 24 carat

⇒18 carat 18/24 = 0.75

Let x = amount of 75% gold required

⇒12 carat= 12/24 = 0.50

⇒(120-x) = amount of 50% gold required

⇒16 carat =16/24 = 2/3

The amount of pure gold equation:

⇒0.75x + 0.50*(120-x) = 2/3*(120)

⇒0.75x + 60 -0.50x = 80

⇒0.75x - 0.50x = 80 - 60

⇒0.25x = 20

⇒x = 20/0.25

⇒x = 80 grms of 18 carat gold

⇒ 120 - 80 = 40 gms of 12 carat gold

⇒40 gms of 12 carat gold .......ANS

Check

⇒0.75x + 0.50*(120-x) = 0.75(80) + 0.50(40) =60 + 20 = 80