Profit and Loss
About 6 min · Elementary Mathematics · English
Time worked out from the lesson's 369 words at 150 words a minute, plus a minute for each question.
Profit and Loss is a core topic in SSC GD Elementary Mathematics. These problems test your ability to quickly manipulate percentages and understand commercial arithmetic.
Key ideas
- Cost Price (CP) is the amount paid to acquire an article. It includes purchase price plus any additional expenses like transport or repair (called overhead expenses).
- Selling Price (SP) is the amount received when the article is sold. Profit or loss is always calculated on the CP, not the SP.
- Profit occurs when SP > CP. Profit = SP − CP. Profit percentage = (Profit / CP) × 100.
- Loss occurs when SP < CP. Loss = CP − SP. Loss percentage = (Loss / CP) × 100.
- Marked Price (MP) is the price tag displayed on the article, often higher than CP. The seller announces discounts on this marked price.
Watch out for
- Calculating profit/loss percentage on SP instead of CP → Always remember: Profit% and Loss% are fractions of CP, not SP. Formula uses CP in denominator.
- Calculating discount percentage on CP or SP instead of MP → Discount% is always (Discount / MP) × 100. MP is the reference, not CP or SP.
- Confusing marked price with cost price → MP is the label price; CP is what the shopkeeper paid. They are usually different. Don't assume MP = CP.
Quick reference
- Profit = SP − CP; Loss = CP − SP (always on CP base)
- Profit% = [(SP − CP)/CP] × 100; Loss% = [(CP − SP)/CP] × 100
- SP when profit: SP = CP(100 + P%)/100; SP when loss: SP = CP(100 − L%)/100
- Discount = MP − SP; Discount% on MP, not CP
- If SP and profit% given, CP = (SP × 100)/(100 + profit%)
Check yourself: 3 questions
1. A shopkeeper bought a calculator for Rs. 360 and sold it for Rs. 432. What is his profit percentage?
2. A trader marks his goods 40% above the cost price and allows a discount of 20%. What is his profit percentage?
3. A shopkeeper sold an article at a loss of 15%. If he had sold it for Rs. 30 more, he would have gained 10%. What is the cost price of the article?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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