Profit & Loss
Profit and loss is percentages applied to trade. Almost every question reduces to picking the right base — cost price or marked price — and the candidates who lose marks here usually lost them by computing a percentage against the wrong one.
Updated 19 September 2026 · Typically 2-4 questions in a service-company aptitude paper.
How to think about profit & loss
Profit percentage is always on cost price
Unless a question explicitly says otherwise, profit % and loss % are calculated on the cost price. Discount %, by contrast, is always calculated on the marked price. Mixing these two bases is the single most common error in this topic.
The marked price chain
A typical question layers three numbers: cost price (what the seller paid), marked price (the sticker), and selling price (what was actually charged after discount). Work in that order and express each as a multiple of CP — set CP = 100 and the algebra disappears.
Equal selling prices always lose
If two items sell for the same price, one at x% profit and the other at x% loss, the net result is always a loss of (x²/100)%. It is never break-even. This is a favourite question because the intuitive answer — zero — is wrong.
Formulas and shortcuts
- Profit
Profit = SP − CP - Profit %
Profit % = ((SP − CP) / CP) × 100 - Selling price from profit %
SP = CP × (100 + p) / 100 - Cost price from selling price
CP = (SP × 100) / (100 + p) - Discount
Discount % = ((MP − SP) / MP) × 100On marked price — not on cost price.
- Same SP, x% profit and x% loss
Net loss % = x² / 100Always a loss, never break-even.
Solved examples
Q1. An article bought for ₹400 is sold for ₹500. Find the profit percentage.
- Profit = SP − CP = 500 − 400 = 100
- Profit % = (Profit / CP) × 100 = (100 / 400) × 100
Answer: 25% profit
Q2. A shopkeeper marks goods 25% above cost price and then allows a 10% discount. What is the net profit percentage?
- Set CP = 100 so the percentages become rupees.
- Marked price = 100 × 1.25 = 125
- Selling price after 10% discount = 125 × 0.90 = 112.5
- Profit = 112.5 − 100 = 12.5 on a cost of 100
Answer: 12.5% profit
Note it is not 25 − 10 = 15%. The discount is taken on 125, not on 100.
Q3. Two articles are each sold for ₹1,200. One is sold at 20% profit and the other at 20% loss. What is the overall result?
- Find each cost price separately — this is where the loss hides.
- CP of the profitable one = 1200 / 1.20 = ₹1,000
- CP of the loss-making one = 1200 / 0.80 = ₹1,500
- Total CP = 1000 + 1500 = ₹2,500. Total SP = 2 × 1200 = ₹2,400
- Loss = 2500 − 2400 = ₹100 on ₹2,500
Answer: An overall loss of ₹100, which is 4%
The shortcut gives the same thing: x²/100 = 400/100 = 4% loss.
Practice questions with answers
1. An item costing ₹250 is sold for ₹300. The profit percentage is:
Answer: B. 20% — Profit = 50. (50 / 250) × 100 = 20%.
2. A article costs ₹600 and is sold at 20% profit. The selling price is:
Answer: C. ₹720 — SP = 600 × 1.20 = ₹720.
3. An article sold for ₹480 at a 20% loss. Its cost price was:
Answer: C. ₹600 — CP = 480 / 0.80 = ₹600. Dividing, not multiplying — the loss applies to CP.
4. An item marked at ₹800 is sold after a 15% discount. The selling price is:
Answer: B. ₹680 — 800 × 0.85 = ₹680.
5. Two items sell at the same price, one at 10% profit and one at 10% loss. The net result is:
Answer: B. 1% loss — x²/100 = 100/100 = 1% loss. Equal selling prices always produce a loss.
6. If the cost price of 100 articles equals the selling price of 80 articles, the profit percentage is:
Answer: B. 25% — Let each SP = 1, so SP of 80 = 80 = CP of 100. CP each = 0.8. Profit = 0.2 on 0.8 → 25%.
7. A trader marks goods 40% above cost and gives a 25% discount. The profit percentage is:
Answer: A. 5% — CP = 100 → MP = 140 → SP = 140 × 0.75 = 105. Profit = 5%.
8. A "buy 3 get 1 free" offer is equivalent to a discount of:
Answer: B. 25% — You pay for 3 and receive 4. Discount = 1/4 = 25% on the marked value of 4 items.
Where marks get lost
- Computing discount on cost price instead of marked price.
- Subtracting the markup and discount percentages directly (25% up then 10% off is not 15% profit).
- Assuming equal selling prices at equal profit and loss percentages break even.
- Multiplying instead of dividing when going from selling price back to cost price.
Reading is not practising.
Run a timed set on profit & loss and see which step you actually lose time on. Free, no card needed.
Start a timed set