CDS 2026 (I) Elementary Mathematics, question 88

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

Q88

What is the percentage of zinc in X ?

(a) $40\%$
(b) $36\%$ Correct answer
(c) $34\%$
(d) $30\%$

Solution.

Answer: (b) $36\%$

Tin fixes the mass fractions as $X:Y = 3:5$ .
If z is the zinc percentage in X, then $(3/8)z + (5/8)4 = 16$ , giving $3z + 20 = 128$ and $z = 36$ .
This also follows from X containing only copper and zinc: $100 - 64 = 36$ .