Ratio, Proportion & Commercial Maths (VI–VIII) • Topic 3 of 5

Profit, Loss & Discount

Cost Price (CP) is what the seller pays; Selling Price (SP) is what the buyer pays. If SP is more than CP there is a profit (gain) of SP − CP; if SP is less than CP there is a loss of CP − SP. The single most important rule — and the most commonly broken one — is that profit% and loss% are ALWAYS calculated on the cost price: Profit% = (Profit / CP) × 100. Marked Price (MP), or list price, is the tag price before any discount; the discount is a reduction on the marked price, so SP = MP − discount and Discount% is always taken on the MP. PEDAGOGY: this topic is the natural place to connect percentages to real shopkeeping, and good teaching uses actual price tags and bills so the abstract CP/SP/MP labels attach to something children have seen. COMMON MISCONCEPTIONS: by far the most frequent error — and a favourite CTET pedagogy target — is computing profit% on the selling price instead of the cost price. Children also confuse marked price with selling price (forgetting the discount), and mix up which of CP/SP is bigger in a loss. HOW TESTED: find SP given CP and profit%, find profit% given CP and SP, and a discount/marked-price calculation, plus a 'spot the child's error' item on the wrong base.

✅ Solved examples

1. An article is bought for ₹250 and sold for ₹300. Find the profit and the profit percent.
Profit = SP − CP = 300 − 250 = ₹50. Profit% = (Profit / CP) × 100 = (50 / 250) × 100 = 20%.
2. A shopkeeper buys a toy for ₹400 and sells it at a loss of ₹40. Find the selling price and the loss percent.
SP = CP − Loss = 400 − 40 = ₹360. Loss% = (40 / 400) × 100 = 10%.
3. The marked price of a shirt is ₹800 and a discount of 25% is given. Find the selling price.
Discount = 25% of 800 = (25/100) × 800 = ₹200. SP = MP − Discount = 800 − 200 = ₹600.
4. A pen costing ₹50 is sold at a profit of 20%. Find the selling price.
Profit = 20% of CP = (20/100) × 50 = ₹10. SP = CP + Profit = 50 + 10 = ₹60.

✏️ Practice — try these, take hints as needed

1. A book is bought for ₹120 and sold for ₹150. Find the profit percent.
Profit = SP − CP.
Profit% is taken on CP, not SP.
30 / 120.
25%
2. An item costing ₹500 is sold for ₹450. Find the loss percent.
Loss = CP − SP = 50.
Loss% on CP.
10%
3. A bag marked at ₹1200 is sold after a 15% discount. Find its selling price.
Discount = 15% of the marked price.
SP = MP − discount.
₹1020 (discount ₹180)
4. A cycle bought for ₹2000 is sold at a profit of 15%. Find the selling price.
Profit = 15% of 2000.
SP = CP + profit.
₹2300 (profit ₹300)

📝 Topic test — 8 questions

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