Profit and Loss Questions: Method and Worked Examples
Profit is on cost price, discount is on marked price. Six original questions show the rest.
Profit and loss questions are about three prices: what the seller paid, what the seller asked for, and what the buyer finally paid. Once you know which price is which, every question is a percentage of the right base.
The one rule that solves most mistakes: profit and loss percentages are always worked out on the cost price, and discount is always worked out on the marked price.
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The Terms You Need
- Cost price (CP)
- What the seller paid for the item. Profit % and loss % are calculated on this.
- Selling price (SP)
- What the buyer actually pays. If SP is more than CP, there is a profit. If less, a loss.
- Marked price (MP)
- The price on the label, before any discount. Also called list price.
- Discount
- The cut from the marked price. Discount % is calculated on MP, not on CP.
- Profit % and loss %
- Profit % = (SP − CP) ÷ CP × 100. Loss % = (CP − SP) ÷ CP × 100.
The Method
- 1
1. Write down which prices you know
Label each number in the question as CP, SP or MP. Many errors come from treating an SP as a CP.
- 2
2. If there is a discount, get SP from MP first
SP = MP − discount. Do this before you think about profit.
- 3
3. Work out profit or loss on CP
Profit % always divides by CP, even when the question gives SP first.
- 4
4. To find CP from SP, divide
If SP is 110% of CP, then CP = SP ÷ 1.10. Do not take 10% off SP.
- 5
5. For mixed deals, use totals
When two items are sold, add both CPs and both SPs, then compare the totals.
Practice Questions With Full Solutions
Original questions written for this page. Try each one before reading the solution.
- 1
Practice question 1: A shopkeeper buys a phone for ₹12,500 and sells it for ₹14,000. Find the profit percentage.
Profit = 14,000 − 12,500 = ₹1,500. Profit % = 1,500 ÷ 12,500 × 100 = 12%. Answer: 12%.
- 2
Practice question 2: A cycle sold for ₹2,700 gives a 10% loss. At what price should it be sold for a 15% profit?
SP is 90% of CP, so CP = 2,700 ÷ 0.90 = ₹3,000. For 15% profit, SP = 3,000 × 1.15 = ₹3,450. Answer: ₹3,450.
- 3
Practice question 3: A jacket is marked ₹1,600. The shop gives a 12.5% discount and still makes a 12% profit. Find the cost price.
Discount is on MP: 12.5% of 1,600 = 200, so SP = ₹1,400. SP is 112% of CP, so CP = 1,400 ÷ 1.12 = ₹1,250. Check: 1,250 × 1.12 = 1,400. Answer: ₹1,250.
- 4
Practice question 4: Two chairs are sold for ₹1,980 each. One gives a 10% profit, the other a 10% loss. Find the overall result.
First chair: CP = 1,980 ÷ 1.10 = ₹1,800. Second chair: CP = 1,980 ÷ 0.90 = ₹2,200. Total CP = ₹4,000. Total SP = ₹3,960. Loss = ₹40, which is 40 ÷ 4,000 × 100 = 1%. Answer: 1% loss.
- 5
Practice question 5: A dealer claims to sell rice at cost price but uses a 900 g weight in place of 1 kg. Find his profit percentage.
He is paid for 1,000 g but gives 900 g. His gain is 100 g on goods that cost him 900 g. Profit % = 100 ÷ 900 × 100 = 11 1/9%, about 11.11%. Answer: 11 1/9%.
- 6
Practice question 6: A trader buys pens at 12 for ₹10 and sells them at 10 for ₹12. Find the profit percentage.
Take 60 pens, a number both 12 and 10 divide. Cost: 60 ÷ 12 × 10 = ₹50. Sale: 60 ÷ 10 × 12 = ₹72. Profit = ₹22. Profit % = 22 ÷ 50 × 100 = 44%. Answer: 44%.
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Common Traps
- check_circleDividing by SP. Profit % is on CP. ₹1,500 profit on a ₹14,000 sale is 12% of CP, not 10.7%.
- check_circleTaking a discount off CP. Discount always comes off the marked price.
- check_circleFinding CP by subtracting. If SP is ₹2,700 after a 10% loss, CP is 2,700 ÷ 0.9 = ₹3,000, not 2,700 + 270 = ₹2,970.
- check_circleAssuming equal profit and loss cancel out. With the same SP and the same percentage, the result is always a loss, because the loss item cost more.
- check_circleGetting false weight upside down. Profit is the weight held back divided by the weight actually given, not by 1 kg.
Why Equal Profit and Loss Gives a Loss
Both items sell for the same price. The one sold at a loss had a higher cost price, so its 10% is a bigger amount in rupees than the 10% earned on the cheaper one. In practice question 4, the loss is ₹220 and the profit is ₹180.
How Bank and SSC Papers Test This
In IBPS PO, profit and loss is listed under arithmetic in the Quantitative Aptitude syllabus (prelims: 35 questions, 30 marks). In mains, the Data Analysis & Interpretation section (40 questions, 60 marks) lists caselet DI, where the cost, marked price and discount of several items are given as a paragraph and you build the table yourself.
In SSC CGL, "Percentage, Profit & Loss" is a listed topic in the Tier 1 Quantitative Aptitude section (25 questions, 50 marks), and it carries into the Tier 2 Mathematical Abilities section.
FAQs
What is the formula for profit percentage?expand_more
Profit % = (SP − CP) ÷ CP × 100. The base is always the cost price.
Is discount calculated on cost price or marked price?expand_more
On the marked price. Profit and loss are on the cost price. Mixing the two is a common mistake.
How do you find cost price from selling price and profit percentage?expand_more
Divide. CP = SP ÷ (1 + profit %/100). For SP ₹1,400 and 12% profit, CP = 1,400 ÷ 1.12 = ₹1,250.
Is profit and loss asked in IBPS PO and SSC CGL?expand_more
Yes. It is a listed arithmetic topic in IBPS PO Quantitative Aptitude and in the SSC CGL Quantitative Aptitude syllabus.
Next steps
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