A grocer purchased 50 kg of rice at ₹40 per kg and 20 kg of another variety of rice at ₹55 per kg. He mixed the two varieties and sold the entire mixture at ₹48 per kg. Find his total profit or loss in this transaction.
- (a)Loss of ₹260
- (b)Loss of ₹240
- (c)Profit of ₹260
- (d)Loss of ₹290
Answer
Why
Correct — C. Price each lot at its own rate, then compare total cost with total sale.
Cost of first lot: 50 × 40 = ₹2,000
Cost of second lot: 20 × 55 = ₹1,100
Total cost: 2,000 + 1,100 = ₹3,100
Total weight: 50 + 20 = 70 kg
Sale: 70 × 48 = ₹3,360
Sale − cost: 3,360 − 3,100 = ₹260 profit → option (c)
Why the others are wrong
- (a)Loss of ₹260 — Right amount, wrong direction. The mixture sells for ₹3,360 and cost ₹3,100, so revenue is above cost: a gain of ₹260, not a loss.
- (b)Loss of ₹240 — A loss is impossible here: the sale brings in ₹3,360 against a cost of ₹3,100. The difference is ₹260 in the grocer's favour, not ₹240 against him.
- (d)Loss of ₹290 — ₹48 is above the average cost per kg of 3,100 ÷ 70 ≈ ₹44.29, so every kilogram of the mixture sells above its cost. No loss of any size is possible.
Concept
On a mixture, profit is total sale minus total cost. The two lots are different sizes, so the plain average of ₹40 and ₹55 (₹47.50) is not the cost per kg.
The true cost per kg is a weighted average: 3,100 ÷ 70 ≈ ₹44.29. The grocer sells at ₹48, above that figure, so the result has to be a profit.
Per-lot check, without totals.
Each kg of the ₹40 rice sells ₹8 above its cost: 50 × 8 = +₹400
Each kg of the ₹55 rice sells ₹7 below its cost: 20 × 7 = −₹140
Net: 400 − 140 = +₹260, the same answer.
Key facts
- Cost of a mixture = sum of (quantity × rate) over its lots.
- Cost per kg of a mixture = total cost ÷ total quantity, which equals the simple average of the rates only when the quantities are equal.
- Profit or loss = total selling price − total cost price, and a positive result means profit.
Study next
Common traps
- Averaging ₹40 and ₹55 to ₹47.50 as if the lots were equal — the 50 kg lot pulls the true cost down to about ₹44.29.
- Reading a loss because the ₹55 variety sells below its cost, and missing that the larger ₹40 lot more than covers it.
Pricing a mixture from its total cost also decides 20 Sep 2025, 12:30, Quant Q.18: 40 L of oil at Rs. 50 and 60 L at Rs. 60 cost Rs. 56 a litre mixed, so 20 L sold at Rs. 70 gives a Rs. 280 profit.
13 Sep 2025, 16:00, Quant Q.4 asks for a percentage instead: coffee at ₹120 and ₹180 mixed 1 : 2 costs ₹160 per kg, so selling at ₹152 is a 5% loss.
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