Profit and loss are always calculated on the cost price unless the question explicitly says otherwise. Discount is always calculated on the marked price. Getting the base right is 90% of the battle.
Core relations
Profit% = (SP − CP)/CP × 100. SP = CP × (1 + Profit%/100). SP after discount = MP × (1 − Discount%/100).
How to Approach It
The whole topic turns on two anchors: profit and loss are measured on the cost price, while discount is measured on the marked price. Keep those bases straight and nothing here can trip you.
- Label CP, MP and SP. Write down which figure is the cost price, marked price and selling price. Most problems hand you two and ask for the third, so the labels keep you oriented.
- Anchor the cost price at 100. When only percentages are given, set CP = 100 and carry MP and SP as plain numbers. The profit percent then reads straight off as SP minus 100.
- Apply each percentage to its own base. Use the cost price for profit and loss, and the marked price for discount. Convert each percentage to a multiplier.
- Flag the classic traps early. Equal selling prices at +x% and −x% give a net loss, not break-even, and successive discounts never simply add.
Techniques & Methods
- Anchor CP at 100. Set cost price = 100, then carry marked price and selling price as plain numbers. e.g. Mark +40%, discount 10% → SP = 126 → 26% profit.
- Equal-price both-ways loss. Same selling price at +x% and −x% always loses (x/10)^2 %. e.g. ±10% → 1% loss overall.
- Discounts as multipliers. Successive discounts d1, d2 → ×(1−d1/100)(1−d2/100). e.g. 20% then 10% → ×0.72 of marked price.
- Faulty-weight gain. Selling x grams as a kilo gives profit = error/(true−error) × 100. e.g. 900 g as 1 kg → 100/900 = 11.1% profit.
The Edge
When two items are sold at the same price, one at x% gain and the other at x% loss, the result is always a loss of (x/10)^2 percent on the whole transaction. Same price, +10% and −10%? Loss = 1%. +20% and −20%? Loss = 4%. The seller never breaks even — recognise this pattern and skip the arithmetic.Worked example
A shopkeeper marks goods 40% above cost and offers a 10% discount. Find the profit percent.
- Anchor everything to cost: let CP = 100.
- Marked 40% above cost → MP = 140.
- Discount is taken on the marked price: SP = 140 × 0.90 = 126.
- Profit is measured on cost: (126 − 100)/100 × 100 = 26%.
Answer: Profit = 26%
Worked example
Two articles are each sold for Rs 99 — one at 10% gain, the other at 10% loss. Find the overall result.
- Same SP with equal % gain and loss is the both-ways trap: always a loss, never break-even, since they act on different cost prices.
- Recover each cost: gain item CP = 99 ÷ 1.10 = 90; loss item CP = 99 ÷ 0.90 = 110.
- Total cost = 90 + 110 = 200; total SP = 198 — a loss of 2 on a cost of 200.
- Loss% = 2/200 × 100 = 1%, matching (x/10)² = (10/10)² = 1%.
Answer: Overall loss = 1%
Worked Drills
Worked example
CP = Rs 250, SP = Rs 300. Profit percent is:
- Profit = 300 − 250 = 50.
- Profit% = 50/250 × 100 = 20%.
Answer: 20% (option c)
Worked example
A man buys 12 articles for Rs 10 and sells 10 for Rs 12. His profit percent is:
- Buy 60 articles: cost = Rs 50. Sell 60 articles: revenue = Rs 72.
- Profit = 72 − 50 = 22 on a cost of 50 → 22/50 × 100 = 44%.
Answer: 44% (option c)
Worked example
Two articles are sold at Rs 2400 each, one at 20% gain and one at 20% loss. The net result is:
- Equal price + equal % gain and loss → loss of (x/10)^2.
- = (20/10)^2 = 4% loss.
Answer: 4% loss (option a)
Worked example
By selling 33 m of cloth, a trader gains an amount equal to the selling price of 11 m. His gain percent is:
- CP of 33 m = SP of 33 m − SP of 11 m = SP of 22 m.
- Gain = SP(11)/SP(22) = 50%.
Answer: 50% (option c)
Worked example
Two articles of equal cost are sold, one at 20% profit and one at 20% loss. The net result is:
- Equal cost (not equal price): the +20% and −20% act on the same base.
- They cancel exactly → no profit, no loss.
Answer: No profit no loss (option a)
Worked example
Goods marked 50% above cost are sold after successive discounts of 20% and 10%. The result is:
- Let CP = 100 → MP = 150. Apply multipliers: 150 × 0.8 × 0.9 = 108.
- SP = 108 on cost 100 → 8% profit.
Answer: 8% profit (option b)
Worked example
An article sold at 12% loss would have given 8% profit if sold for Rs 92 more. The cost price is:
- The Rs 92 covers the gap from −12% to +8%, i.e. 20% of CP.
- 20% of CP = 92 → CP = 460.
Answer: Rs 460 (option c)
Worked example
A dealer sells at cost price but uses a 900 g weight for 1 kg. His profit percent is:
- Profit = error/(true − error) × 100 = 100/(1000 − 100) × 100.
- = 100/900 × 100 = 11.11%.
Answer: 11.11% (option b)
Worked example
A shopkeeper gives a 10% discount yet gains 17%. His marked price is above cost by:
- Let CP = 100 → SP = 117. SP = 0.9 × MP → MP = 117/0.9 = 130.
- MP is 30% above cost.
Answer: 30% (option c)
⚠ Watch out
- Discount is on marked price, profit is on cost price — never mix the bases.
- Selling at the same price with equal % gain and loss is a net loss, never break-even.
- "Profit of Rs 50" is an amount; "profit of 50%" is a ratio — read carefully.
Takeaways
- Two anchors. Profit/loss on cost price; discount on marked price — keep them separate.
- Set CP = 100. Percentages become plain numbers you read straight off.
- Equal price both ways = loss. (x/10)² percent, never break-even.
- Discounts multiply, not add. 20% then 10% is 28% off, not 30%.