Profit and Loss
About 7 min · Numerical and Mathematical Ability · English
Time worked out from the lesson's 459 words at 150 words a minute, plus a minute for each question.
This topic tests your ability to calculate buying price, selling price, discounts, and profit or loss percentages in commercial transactions. Questions range from straightforward single-step calculations to multi-step problems involving marked price, successive discounts, and cost price recovery.
Key ideas
- Cost Price (CP): The price at which an article is purchased or manufactured. All profit and loss calculations use CP as the reference base unless stated otherwise.
- Selling Price (SP): The price at which an article is sold to the customer. Profit occurs when SP > CP; loss occurs when SP < CP.
- Profit and Loss Amounts: Profit = SP − CP (when SP > CP). Loss = CP − SP (when CP > SP). These are absolute amounts in rupees.
- Profit % and Loss %: Always calculated on Cost Price unless explicitly stated otherwise. Profit % = (Profit / CP) × 100. Loss % = (Loss / CP) × 100.
- Marked Price (MP): The label price or list price printed on an article before any discount is applied. Retailers mark up goods above CP to allow room for discounts while still making profit.
Watch out for
- Calculating Profit % on SP instead of CP: Students often compute (Profit / SP) × 100 instead of (Profit / CP) × 100. Always remember: unless stated otherwise, profit and loss percentages are on Cost Price. Fix: Memorize that the denominator in Profit % and Loss % is always CP.
- Adding successive discounts directly: Applying 20% + 10% = 30% discount is wrong. Discounts compound, not add linearly. Fix: Use the formula: d₁ + d₂ − (d₁ × d₂)/100 or apply each discount sequentially.
- Confusing Discount % base: Discount % is always calculated on Marked Price, not Cost Price. Mixing these up scrambles the entire calculation. Fix: Write down MP, apply discount to get SP, then relate SP and CP separately.
Quick reference
- Profit % and Loss % are always on Cost Price (CP) unless otherwise mentioned.
- SP = CP + Profit = CP − Loss. Rearrange to find any unknown.
- Discount is on Marked Price (MP), not CP.
- Successive discounts d₁% and d₂%: Single discount = d₁ + d₂ − (d₁ × d₂)/100.
- If an item is sold at x% profit then x% loss, net effect is a loss of (x²/100)%.
Check yourself: 3 questions
1. A shopkeeper buys an article for Rs 500 and sells it for Rs 650. What is his profit percentage?
2. A trader marks his goods 40% above the cost price and allows a discount of 25% on the marked price. What is his profit or loss percentage?
3. By selling an article for Rs 720, a man loses 10%. At what price should he sell it to gain 15%?
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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