Question

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

Answer 1

Let the weight of 18 carat gold bar be x and 16 carat gold be y.
Then, x + y = 120 .......(1)
Also 18x + 12y = 16*120
18x + 12y = 1920
3x + 2y = 320 (on dividing by 6) ......(2)
Now multiply eq(1) by 2.
2x + 2y = 240. ....(3)
On subtracting eq (3) from (2) we get
x = 80
Put this value in eq (1)
80 + y = 120
y = 120 - 80
y = 40
Therefore, 80g is to be melted from 18carat gold bar and 40g is to be melted from 16 carat gold bar
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