Q.9 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)?
(A) 5:4
(B) 3:4
(C) 3:2
(D) 1:1

The correct ratio of potatoes P:Q by weight is 5:4, yielding exactly 8% profit when mixed and sold at ₹192 per kg.​

Cost Prices

Variety P costs ₹800 for 5 kg, so ₹160 per kg. Variety Q costs ₹800 for 4 kg, so ₹200 per kg. For 8% profit on ₹192 selling price per kg, the mixture’s cost price must be ₹192 / 1.08 = ₹177.78 per kg.​

Option Analysis

Test each ratio for the mixture’s cost price and resulting profit percentage on 1 kg total mix sold at ₹192.

Mixture Method

Assume 5 kg P and 4 kg Q (total 9 kg). Total cost: (5×160) + (4×200) = ₹800 + ₹800 = ₹1600. Cost per kg: ₹1600/9 = ₹177.78. Selling 9 kg at ₹192/kg yields ₹1728 revenue. Profit: ₹1728 – ₹1600 = ₹128, or (128/1600)×100 = 8%.​

A business person buys potatoes of two varieties P and Q, mixes them in a certain ratio, and sells at ₹192 per kg for 8% profit—classic GATE 2025 aptitude question on potatoes P Q mixing ratio 8% profit. Variety P costs ₹800 for 5 kg (₹160/kg), Q costs ₹800 for 4 kg (₹200/kg).​

Step-by-Step Solution

First, calculate required mixture cost price: Selling price ₹192 at 8% profit means CP = 192 ÷ 1.08 = ₹177.78/kg. Use weighted average for ratios: CP_mix = (P_kg × 160 + Q_kg × 200) / total kg. The ratio matching ₹177.78 exactly is 5:4.​

Verification with 9 kg mix (5P + 4Q): Cost ₹1600, sell ₹1728, profit ₹128 (8%).​

Why Other Options Fail

• 3:4: CP ₹182.86/kg → 5% profit (too low).​

• 3:2: CP ₹176/kg → 9.09% profit (too high).​

• 1:1: CP ₹180/kg → 6.67% profit (too low).​

This potatoes P Q mixing ratio 8% profit problem tests alligation basics for CSIR NET/GATE prep. Practice similar mixture-profit questions for exams.​