A shopkeeper sells rice at the rate of ₹44 per kg whose cost price is ₹40 per kg. Not satisfied with this, he tries to increase his profit by removing 200 grams of rice from each packet. What is the shopkeeper’s overall gain percentage?
- (a)
- (b)
- (c)
- (d)
Answer
Why
Correct — B. Price one packet that the customer pays for as a full kilogram.
Revenue is the 1 kg rate: ₹44
The packet actually holds 1,000 − 200 = 800 g.
Cost of 800 g at ₹40 per kg = 0.8 × 40 = ₹32
Profit = 44 − 32 = ₹12
Gain% = profit / cost = 12 / 32 × 100 = 37.5% → option (b).
Why the others are wrong
- (a)35% is the 10% mark-up and the 25% short weight simply added together. Percentages taken on different bases do not add, which is why the packet has to be priced instead.
- (c)37% is 37.5% rounded down, but nothing in the working rounds: 12 divided by 32 is exactly 0.375. An option half a point away is there to catch an estimate.
- (d)35.5% would need a profit of ₹11.36 on a cost of ₹32, and no combination of ₹44, ₹40 and 800 g gives that figure.
Concept
Two sources of profit stack here, and the safe method is to price one packet rather than to combine percentages.
Revenue is fixed by what the customer pays for a nominal kilogram: ₹44.
Cost is fixed by what the shopkeeper actually parts with: 800 g, costing 0.8 × 40 = ₹32.
Gain percentage is profit over cost, so 12 / 32 = 37.5%. The denominator is 32 and not 40 — using 40 gives 30%, and that is the standard slip in false-weight questions.
All four options are printed as images rather than text: they read 35%, 37.5%, 37% and 35.5%, with 37% sitting half a point from the answer to punish a rounded estimate.
Key facts
- Removing 200 g from a 1 kg packet leaves 800 g, whose true cost is 0.8 × 40 = ₹32.
- Gain percentage is profit divided by cost price, not by selling price and not by the list rate.
- Revenue ₹44 against cost ₹32 is a profit of ₹12, which is 37.5% of 32.
- A short weight raises the gain even at an unchanged selling rate, because it shrinks the cost side.
Study next
Common traps
- Dividing the ₹12 profit by ₹40 rather than by the ₹32 actually spent
- Adding the 10% mark-up to the 25% short weight to reach 35%
- Reading removing 200 grams as handing over 1,200 g for the price of one kilogram
SSC pairs an honest mark-up with a dishonest weight and asks for the combined gain. Comparable items are asked 19 Sep 2024, 09:00, Quant Q.1, where a reduced rate meets a faulty weight, and 26 Sep 2024, 16:00, Quant Q.4, a 100 g fault in a 3 kg weight.
Related PYQs
No directly related past PYQ was found.