840 g gold and 350 g silver are heated in a furnace and their molten forms are mixed to form a homogeneous alloy. X g alloy is sold out and after that the remaining alloy is heated again and 150g is mixed with it. Find the value of x, if the ratio of gold and silver in the final alloy becomes 3:23:2.
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Adding data: 150 g silver is mixed in the end
To find: the value of x
Solution:
Initially, gold : silver = 840 : 350 = 12 : 5
Given, x g alloy is sold out.
In x g alloy,
gold = 12x/17 g & silver = 5x/17 g
Gold left = 840 - 12x/17 g
Silver left = 350 - 5x/17 g
Now 150 g silver is mixed
Silver = 350 - 5x/17 + 150 = 500 - 5x/17 g
Given,
840 - 12x/17 : 500 - 5x/17 = 3 : 2
or, (840 - 12x/17) / (500 - 5x/17) = 3 / 2
or, 1680 - 24x/17 = 1500 - 15x/17
or, 9x/17 = 180
or, x = 180 * 17 / 9
or, x = 340
Answer: Value of x is 340 g.
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