Multiple choice

Two metals 'X' and 'Y' are to be used for making two different alloys. If the ratio (by weight) of 'X' and 'Y' in the first alloy is 6 : 5 and that in the second alloy is 7 : 13, how many kilograms of metal 'X' must be melted along with 11 kg of the first alloy and 20 kg of the second, so as to produce a new alloy containing 40% of metal 'Y'?

  1. 11 kg

  2. 13 kg

  3. 14 kg

  4. 16 kg

  5. 18 kg
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C Correct answer
Explanation

First alloy: 11kg total, X:Y = 6:5 (6kg X, 5kg Y). Second alloy: 20kg total, X:Y = 7:13 (7kg X, 13kg Y). Total X = 6 + 7 + m, Total Y = 5 + 13 = 18. New alloy contains 40% Y, so 60% X. 18 is 40% of total mass, so total mass = 45kg. X = 0.6 * 45 = 27kg. 13 + m = 27, so m = 14.

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