A shopkeeper has a fault of 100 g in a 3 kg weight. He sold 3 kg of potatoes to Charu using the same faulty weight for ₹46. The cost price of the potatoes for the seller was ₹12 per kg. How much profit (in ₹) did he earn on the potatoes?
- (a)11.6
- (b)11.2
- (c)10.2
- (d)10
Answer
Why
Correct — B. The fault sits in what he hands over, not in what he charges.
His "3 kg" weight is short by 100 g, so Charu gets 3,000 − 100 = 2,900 g = 2.9 kg
Cost to the shopkeeper = 2.9 × 12 = ₹34.80
He was paid ₹46
Profit = 46 − 34.80 = ₹11.20
That is option (b).
Why the others are wrong
- (a)11.6 — ₹11.60 would need the potatoes to have cost ₹34.40, that is under 2.87 kg. The faulty weight is short by a flat 100 g, so exactly 2.9 kg leaves the shop.
- (c)10.2 — ₹10.20 implies a cost of ₹35.80, or 2.983 kg of potatoes. Nothing in the question shortens the weight by 17 g — the stated fault is 100 g.
- (d)10 — ₹10 is the honest-shopkeeper answer: ₹46 taken against 3 × 12 = ₹36 of cost. It ignores the 100 g he charged for and never delivered.
Concept
A false weight works on the cost side of the deal. The customer pays for 3 kg, but the shopkeeper parts with only 2.9 kg, so he sells more than he buys.
Rupee profit is then just money in minus money out: ₹46 received against ₹34.80 of potatoes actually surrendered.
The familiar formula gain% = error ⁄ (true weight − error) × 100 applies only when goods are sold at cost price. That is not the case here — ₹46 for a nominal 3 kg is already above the ₹36 those 3 kg would cost.
Two separate gains are stacked in this item, and separating them checks the answer.
He charges ₹46 for what he calls 3 kg of ₹12 potatoes, which is ₹10 of ordinary profit. He then withholds 100 g, worth ₹1.20 at ₹12 per kg.
₹10 + ₹1.20 = ₹11.20, matching the subtraction exactly.
Key facts
- A 100 g fault in a 3 kg weight delivers 2.9 kg, so the seller's cost falls to 2.9 × ₹12 = ₹34.80.
- Rupee profit is receipts minus the cost of the goods actually handed over.
- The withheld 100 g is worth ₹1.20, exactly the gap between the honest profit of ₹10 and the actual ₹11.20.
Study next
Common traps
- Costing the full 3 kg at ₹36 and answering ₹10.
- Reading the fault as 100 g per kilogram, which would put the delivery at 2.7 kg.
- Answering with a percentage when the question asks for rupees.
False weights arrive either as a rupee profit like this one or as a gain percentage — see 11 Sep 2024, 09:00, Quant Q.3 (weights 12% below true, 10% profit) and 19 Sep 2024, 09:00, Quant Q.1 (a 900 g weight used after a price cut).
Related PYQs
No directly related past PYQ was found.