Three varieties of rice costing ₹40/kg, ₹50/kg, and a third unknown price are mixed in the ratio 2:3:5. If the resulting mixture is sold at ₹55/kg, making a profit of 10% on the cost price, what is the price of the third variety of rice per kg?

Correct — C. First recover the mixture's cost from its selling price.

Sold at ₹55 with a 10% profit: CP = 55 ÷ 1.1 = ₹50 a kg

Take 10 kg in the ratio 2 : 3 : 5, costing 10 × 50 = ₹500
Known varieties: 2 × 40 + 3 × 50 = 80 + 150 = ₹230
Third variety: its 5 kg cost 500 − 230 = ₹270

Price a kg = 270 ÷ 5 = ₹54 → option (c)

Why the others are wrong

• (a)
  ₹52.50 — The mix would cost (230 + 5 × 52.5) ÷ 10 = ₹49.25 a kg, and a 10% profit on that is about ₹54.18, not ₹55.
• (b)
  ₹57.50 — The mix would cost (230 + 287.5) ÷ 10 = ₹51.75 a kg, so selling at ₹55 would earn about 6.3%, not 10%.
• (d)
  ₹62.50 — The mix would cost (230 + 312.5) ÷ 10 = ₹54.25 a kg, leaving a margin under 1.4% at ₹55, far from 10%.

A mixture sold at a profit has two layers. First strip the profit: cost = selling price ÷ (1 + profit%). Only that cost is the weighted average of the ingredients.

Then write the weighted average: (2 × 40 + 3 × 50 + 5x) ÷ 10 = 50. That gives 5x = 270 and x = ₹54. The ₹55 is never averaged; it sits on the selling side.

Key facts

• Cost of a mixture = selling price ÷ (1 + profit⁄100): 55 ÷ 1.1 = 50.
• Weighted average cost = Σ(quantity × price) ÷ Σ quantity.
• With the third variety at ₹54, the 10 kg cost 80 + 150 + 270 = ₹500.

Common traps

• Treating ₹55 as the cost: (230 + 5x) ÷ 10 = 55 gives x = ₹64, not an option.
• Taking 10% off ₹55 instead of dividing by 1.1: a cost of ₹49.50 gives x = ₹53.

No directly related past PYQ was found.