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GATE 2025 CE (CE2) – Question 9

General Aptitude · Quantitative Aptitude: 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)?

  1. 5:4
  2. 3:4
  3. 3:2
  4. 1:1

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Show answer and explanation

Correct answer: (A) 5:4

Explanation

The cost of P is ₹160/kg and of Q is ₹200/kg. The selling price of ₹192/kg gives 8% profit, so the cost of the mixture is $\frac{192}{1.08} = 177.78$ per kg. If the fraction of P is $x$, then $160x + 200(1 - x) = 177.78$, so $x = \frac{22.22}{40} = \frac{5}{9}$ and the ratio P:Q is 5:4.