Percentage, Profit and Loss
About 6 min · Everyday Mathematics · English
Time worked out from the lesson's 365 words at 150 words a minute, plus a minute for each question.
Percentage, profit and loss is a topic in the SOF IMO Everyday Mathematics section. These problems appear across Classes 8–10 and form the backbone of commercial arithmetic questions. Students must master converting fractions and decimals to percentages, computing profit/loss from cost price (CP) and selling price (SP), understanding marked price (MP) and discount, and solving multi-step problems involving successive percentages or transaction chains.
Key ideas
- Percentage means "per hundred" and is denoted by %. To convert a fraction to percentage, multiply by 100. To convert percentage to fraction, divide by 100.
- Cost Price (CP) is the price at which an article is purchased. Selling Price (SP) is the price at which it is sold. Profit or loss is always calculated on CP unless stated otherwise.
- Profit occurs when SP > CP. Profit = SP − CP. Loss occurs when SP < CP. Loss = CP − SP.
- Marked Price (MP) is the printed or list price on an article. Discount is the reduction offered on MP. Selling Price after discount: SP = MP − Discount.
- Successive percentages are not additive. If two discounts or changes are applied one after another, you must apply them sequentially, not by adding percentages. For example, 10% discount followed by 20% discount is not 30% discount.
Quick reference
- Profit = SP − CP; Loss = CP − SP
- Profit % = (Profit/CP) × 100; Loss % = (Loss/CP) × 100
- SP = CP × (100 ± Profit or Loss %)/100
- Discount % is on MP, not SP: SP = MP × (100 − Discount %)/100
- Successive discounts: multiply the remaining percentages sequentially
Check yourself: 3 questions
1. A shopkeeper marks his goods 25% above the cost price and then gives a discount of 10%. What is his actual profit percentage?
2. The price of a mobile phone is first increased by 20%, then decreased by 15%, and finally increased by 10%. If the final price is Rs 11,220, what was the original price of the mobile phone?
3. A fruit vendor marks his fruits 40% above the cost price but gives a discount of 15% on the marked price. What is his actual profit percentage?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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