Suman purchased 25 liters of milk at ₹45 per liter and another 15 liters of milk at ₹50 per liter. She combined both quantities and then sold the entire mixture at ₹48 per liter. What was her total profit or loss?

Correct — B. Compare what she paid with what she received.

First lot = 25 × 45 = ₹1,125
Second lot = 15 × 50 = ₹750
Total cost = ₹1,875 for 40 L

Revenue = 40 × 48 = ₹1,920
Profit = 1,920 − 1,875 = ₹45 → option (b).

Why the others are wrong

• (a)
  Loss of ₹45 — Right size, wrong direction. Revenue of ₹1,920 exceeds the ₹1,875 cost, so the ₹45 is a gain. Selling above the ₹46.875 average cost cannot produce a loss.
• (c)
  Profit of ₹90 — Per litre: +₹3 on 25 L = ₹75, −₹2 on 15 L = −₹30, net ₹45. A ₹90 profit would need a selling price of ₹49.125 a litre, not ₹48.
• (d)
  Loss of ₹90 — Wrong on both counts. The sale brings in ₹45 more than the ₹1,875 cost, so there is a profit, and it is ₹45, not ₹90.

Mixing changes neither the total cost nor the total quantity, so profit on a mixture is total revenue − total cost.

The mixture's cost price is a weighted average: ₹1,875 ÷ 40 = ₹46.875 a litre. It sits nearer ₹45 because more of the ₹45 milk went in.

Selling at ₹48 earns ₹1.125 a litre, and 40 × 1.125 = ₹45 — the same answer by a second route.

Key facts

• Mixture cost price = total cost ÷ total quantity, a weighted average of the component prices.
• Here the mixture costs ₹1,875 ÷ 40 = ₹46.875 a litre.
• Profit = revenue − cost: ₹1,920 − ₹1,875 = ₹45.

Common traps

• Averaging ₹45 and ₹50 to ₹47.50 without weighting by quantity, which gives a profit of only ₹20.
• Comparing ₹48 with ₹50 alone and calling the deal a loss, forgetting the cheaper 25 litres.

No directly related past PYQ was found.