An alloy P contains 20% copper and 80% zinc by weight. Another alloy Q contains 60% copper and 40% zinc by weight. A third alloy R is to be prepared from P and Q so that it contains equal amount of copper and zinc. In what ratio, amounts of P and Q be mixed in order to get R?

(a) 1 : 3 ✓ UPSC's answer
(b) 3 : 1
(c) 2 : 3
(d) 3 : 2

Why the answer is (a)

• Let the amount of alloy P be $x$ and alloy Q be $y$.

• The amount of copper in the mixture is $0.20x + 0.60y$.

• The amount of zinc in the mixture is $0.80x + 0.40y$.

• For equal amounts of copper and zinc, set the expressions equal: $0.20x + 0.60y = 0.80x + 0.40y$.

• Rearranging the terms gives $0.20y = 0.60x$, which simplifies to $y = 3x$.

• Therefore, the ratio of P to Q is $x : y = 1 : 3$, matching option (a).

Why the other options are wrong

(b) 3 : 1: This ratio implies 3 parts P and 1 part Q, which results in a mixture with significantly more zinc than copper.
(c) 2 : 3: This ratio implies 2 parts P and 3 parts Q, which results in a mixture with more copper than zinc.
(d) 3 : 2: This ratio implies 3 parts P and 2 parts Q, which results in a mixture with more zinc than copper.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.