A seller sold 19 cookies for ₹95 instead of 20 cookies in one kg, cheating a customer. What is the gain (in ₹) if the seller bought the cookies for ₹76?
- (a)22.8
- (b)28.2
- (c)26.2
- (d)25.8
Answer
Why
Correct — A. One kilogram is 20 cookies and cost the seller ₹76, so his cost per cookie is 76 ⁄ 20 = ₹3.80.
He hands over only 19 cookies, so what actually leaves the shop cost him 19 × 3.80 = ₹72.20.
He still charges the full kilogram price, ₹95.
Gain = 95 − 72.20 = ₹22.80 → option (a).
Why the others are wrong
- (b)28.2 — 28.2 is 22.80 with its digits shuffled. It would need the 19 cookies to have cost ₹66.80, but at ₹3.80 each they cost ₹72.20.
- (c)26.2 — 26.2 implies a cost of ₹68.80 for the 19 cookies, which works out at ₹3.62 each. The cost per cookie is fixed at 76 ⁄ 20 = ₹3.80.
- (d)25.8 — 25.8 implies a cost of ₹69.20, that is ₹6.80 shaved off the ₹76. The short weight is one cookie, so only ₹3.80 comes off.
Concept
Under-weighing questions come in two shapes and are not solved the same way.
When a percentage profit is asked and the goods go out at cost price, the shortcut applies: profit % = (true weight − weight given) ÷ weight given × 100.
This one asks for a rupee gain, so no formula is needed. Cost what actually left the shop, subtract it from what was actually collected, and the difference is the answer.
The cheating is worth exactly one cookie: an honest 20-for-₹95 sale gains ₹19, and holding back one cookie adds its ₹3.80 of cost to the margin, giving ₹22.80.
The stem is compressed, so read ₹76 as the cost of the full kilogram of 20 cookies. Taking it as the cost of the 19 delivered would give ₹19, which no option offers.
Key facts
- Cost per cookie = ₹76 ÷ 20 = ₹3.80.
- The 19 cookies handed over cost the seller ₹72.20 and fetched ₹95.
- Rupee gain = money collected − cost of what was actually handed over.
- Selling at cost price on a short weight gives profit % = (true weight − weight given) ÷ weight given × 100.
Study next
Common traps
- Reading ₹76 as the cost of the 19 cookies delivered, which returns ₹19 and matches no option.
- Costing all 20 cookies when only 19 left the shop.
- Switching to percentages when the question asks for rupees.
A dishonest-dealer item either shorts the weight at the stated price or inflates the price on the stated weight, and the options are usually rearrangements of the right figure.
The short-weight version is asked on 13 Sep 2024, 12:30, Quant Q.16, where a seller gives 800 g instead of 1 kg of rice. Profit-and-loss arithmetic is also set at Quant Q.4 of this shift, which recovers a marked price from a 20% discount.
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