Last reviewed 16 Sept 2026 · 5 min read
Basic terms
| Term | Meaning |
|---|---|
| Cost price (CP) | Price at which an article is bought (including overheads such as transport, repairs, installation) |
| Selling price (SP) | Price at which it is sold |
| Profit (gain) | SP − CP (when SP > CP) |
| Loss | CP − SP (when CP > SP) |
| Marked price (MP) / list price | Price labelled on the article |
| Discount | Reduction on MP: Discount = MP − SP |
Formulas
- Profit % ; Loss % (always on CP unless stated)
- ;
- ;
- Discount % (on MP)
- Relation:
Two successive discounts d₁% and d₂% are equivalent to a single discount of
(Order of discounts does not matter.)
Special cases
1. Two articles sold at the same SP, one at x% gain and the other at x% loss: Overall loss (always a loss)
2. Dishonest dealer (false weights) selling at CP:
3. Dealer using false weight and also marking up/selling above CP: combine as successive percentages, or compare actual cost of goods given with money received.
4. Articles bought at "a for ₹ x" and sold at "b for ₹ y": compute CP and SP per article (or for LCM number of articles).
5. If CP of x articles = SP of y articles: Gain/loss % (gain if x > y)
6. Profit on SP: if profit is p% of SP, then profit on CP
Worked examples
A contractor buys a mixer for ₹ 45 000, spends ₹ 5000 on repairs and sells it for ₹ 60 000. Find the profit percentage.
Solution. CP = 50 000; profit = 10 000 → 20%
By selling a tool for ₹ 1140, a trader loses 5%. Find the CP and the SP for a 5% gain.
Solution. ₹ 1200; SP for 5% gain = ₹ 1260
An article is marked 40% above CP and sold at 15% discount. Find profit %.
Solution. Let CP = 100 → MP = 140 → SP = → 19% profit
A shopkeeper wants 20% profit after allowing 10% discount. By what percent above CP should he mark the goods?
Solution. → mark 33.33% above CP
Find the single discount equivalent to successive discounts of 20% and 10%. What is the SP of an item marked ₹ 2500?
Solution. 28%; SP ₹ 1800
Two plots are sold for ₹ 99 lakh each, one at 10% gain and the other at 10% loss. Find the overall result.
Solution. Loss 1% (CPs: 90 lakh and 110 lakh; total CP 200, SP 198 → loss 2 lakh = 1% ✓)
A dealer claims to sell sand at cost price but uses a 900 kg weight for 1 tonne. Find his gain.
Solution. 11.11%
Oranges are bought at 6 for ₹ 50 and sold at 5 for ₹ 50. Find gain %.
Solution. CP of 30 oranges = ₹ 250; SP of 30 = ₹ 300 → 20% gain (Or: CP per orange 8.33, SP 10 → 20%.)
The CP of 20 articles equals the SP of 16 articles. Find gain %.
Solution. 25% gain
A trader earns a profit equal to 20% of the selling price. What is his profit percentage on cost?
Solution. 25%
Frequently tested points
- Profit/loss % on CP; discount % on MP.
- SP = CP(100 ± p)/100; CP = 100 × SP/(100 ± p).
- MP/CP = (100 + profit%)/(100 − discount%).
- Successive discounts: d₁ + d₂ − d₁d₂/100.
- Same SP with x% gain and x% loss → loss of x²/100 %.
- False weight gain = (true − false)/false × 100.
- CP of x articles = SP of y articles → (x − y)/y × 100.
- Profit p% of SP → p/(100 − p) × 100 % of CP.
- Include overheads in CP.
- Calculating profit percentage on SP when CP is intended.
- Adding successive discounts directly.
- Ignoring repair or transport costs in CP.
- Profit and loss compare selling price with cost price (including overheads), expressed as percentages of CP.
- SP and CP are interconverted using (100 ± p)/100 factors.
- Discounts are calculated on marked price, and MP/CP depends on desired profit and discount.
- Successive discounts combine as d₁ + d₂ − d₁d₂/100.
- Special cases — equal SP with equal gain and loss, false weights, bulk buying and profit on SP — follow standard shortcuts.