GATE 2025 MN – Question 9

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

A business person buys potatoes of two different varieties P and Q, mixes them in a certain ratio and sells them at ₹ 192 per kg.
The cost of the variety P is ₹ 800 for 5 kg.
The cost of the variety Q is ₹ 800 for 4 kg.
If the person gets 8% profit, what is the P:Q ratio (by weight)?

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Correct answer: (A) 5:4

Explanation

Convert the purchase prices to a common unit: P costs 800/5=160 rupees/kg, while Q costs 800/4=200 rupees/kg.

An 8% profit is measured on cost, so the mixture's cost is
$$C=\frac{192}{1.08}=\frac{1600}{9}\ \text{rupees/kg}.$$
If the weights are p and q, then 160p+200q=(1600/9)(p+q). Multiplying by nine and rearranging gives 200q=160p, so **P:Q=5:4, A**.

Check: five kg of P and four kg of Q cost 1600 rupees for nine kg; selling at 192 yields 1728, a profit of 128/1600=8%. Keeping exact fractions avoids rounding the mixture cost prematurely.

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