CDS 2026 (I) Elementary Mathematics, question 87

Topic: Arithmetic (percentage, ratio, interest, time and work, speed)

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Passage · Q87 to Q88

X is an alloy of copper and zinc. Y is an alloy containing 80%80\% of copper, 4%4\% of zinc and 16%16\% of tin. A fused mass of X and Y is found to contain 74%74\% of copper, 16%16\% of zinc and 10%10\% of tin.

Q87

What is the percentage of copper in X ?

  1. (a) 60%60\%
  2. (b) 64%64\%Correct answer
  3. (c) 66%66\%
  4. (d) 70%70\%

Solution.

Answer: (b) 64%64\%

  1. Only alloy Y contains tin.
  2. Since the final tin content is 10% and Y has 16% tin, Y makes up 10/16=5/810/16 = 5/8 of the mixture; X makes up 3/83/8.
  3. If c is the copper percentage in X, then (3/8)c+(5/8)80=74(3/8)c + (5/8)80 = 74.
  4. Multiplying by 8 gives 3c+400=5923c + 400 = 592, so c=64c = 64.
  5. Shortcut: A component absent from one alloy, here tin, determines the mixing ratio immediately.