One type of pulses is sold for ₹72 per kg at a 20% profit. Another type is sold for ₹60 per kg at a 25% profit. If these two varieties are mixed in the ratio of 2:1 (first variety to second variety) and the mixture is sold at ₹70 per kg, what is the overall profit or loss percentage?

Correct — C. Recover each cost price from its selling price, then cost the mixture.

First type: CP = 72 ÷ 1.20 = ₹60 per kg
Second type: CP = 60 ÷ 1.25 = ₹48 per kg

Cost of 3 kg in the ratio 2 : 1 = 2 × 60 + 1 × 48 = ₹168
Cost per kg = 168 ÷ 3 = ₹56

Profit per kg = 70 − 56 = ₹14
Profit % = 14 ÷ 56 × 100 = 25% → option (c).

Why the others are wrong

• (a)
  Profit of 50% — A 50% profit on the ₹56 cost would need a selling price of ₹84 a kg. At ₹70 the mixture sells 25% above cost.
• (b)
  Loss of 25% — ₹70 is above the ₹56 cost, so the sale makes a profit, not a loss. A 25% loss would mean selling at ₹42 a kg.
• (d)
  Loss of 50% — Wrong direction and wrong size. Selling at ₹70 against a ₹56 cost is a gain, and a 50% loss would mean selling at ₹28 a kg.

Profit is a percentage of cost, so CP = SP ÷ (1 + profit%). You divide ₹72 by 1.20; you do not take 20% off it.

Once each cost is known, the mixture's cost per kg is a weighted average by the mixing ratio: (2 × 60 + 1 × 48) ÷ 3 = ₹56.

The profit percentage is then measured on that cost: 14 ÷ 56 = 25%.

Key facts

• ₹72 at a 20% profit comes from a ₹60 cost, since 60 × 1.2 = 72.
• ₹60 at a 25% profit comes from a ₹48 cost, since 48 × 1.25 = 60.
• The 2 : 1 mixture costs ₹56 a kg, so selling at ₹70 gains ₹14 a kg.

Common traps

• Taking 20% off ₹72 (₹57.60) and 25% off ₹60 (₹45) instead of dividing — the profit then comes out near 31%, which is not offered.
• Averaging the selling prices, (2 × 72 + 60) ÷ 3 = ₹68, as if they were costs.
• Dividing the ₹14 profit by the ₹70 selling price, which gives 20%.

No directly related past PYQ was found.