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Question
A jeweler 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 120gm? (Given: Pure gold is 24-carat).
Solution
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 ×16)/24`
⇒3x + 2y = 320 …………(i)
And
x + y = 120 …………(ii)
Multiplying (ii) by 2 and subtracting from (i), we get
x = 320 – 240 = 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.
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