Profit and Loss
1. Basic Terms
| Term | Meaning |
|---|---|
| Cost Price (CP) | The price at which an article is BOUGHT |
| Selling Price (SP) | The price at which an article is SOLD |
| Overhead Expenses | Additional costs (transport, repair, tax) — ADDED to CP |
| Marked Price (MP) | The price TAGGED on the article (list price) |
| Discount | Reduction offered on the marked price |
Rule: Overhead expenses are ALWAYS added to the cost price. Effective CP = Purchase price + Overhead expenses.
2. Profit and Loss Formulas
Profit
If SP > CP: Profit = SP — CP Profit % = (Profit / CP) × 100%
Loss
If SP < CP: Loss = CP — SP Loss % = (Loss / CP) × 100%
'Profit or loss percentage is ALWAYS calculated on the COST PRICE, NOT on the selling price.'
Worked Example: A trader bought a watch for Rs 800 and sold it for Rs 960. Find the profit percentage.
Profit = 960 — 800 = 160 Profit % = (160/800) × 100 = 20%
Worked Example: A shopkeeper bought a table for Rs 1200 and sold it for Rs 1050. Find the loss percentage.
Loss = 1200 — 1050 = 150 Loss % = (150/1200) × 100 = 12.5%
3. Finding SP or CP When Profit/Loss % is Given
Finding SP
SP = (100 + Profit%) / 100 × CP SP = (100 — Loss%) / 100 × CP
Worked Example: Find the SP of an article whose CP is Rs 500 and profit is 15%.
SP = (100 + 15)/100 × 500 = 115/100 × 500 = Rs 575
Finding CP
CP = 100 / (100 + Profit%) × SP CP = 100 / (100 — Loss%) × SP
Worked Example: By selling a chair for Rs 690, a carpenter loses 8%. Find the CP.
CP = 100/(100 — 8) × 690 = 100/92 × 690 = Rs 750
Worked Example: A merchant sold a radio for Rs 840, gaining 20%. Find the CP.
CP = 100/(100 + 20) × 840 = 100/120 × 840 = Rs 700
4. Discount and Marked Price
Discount = Marked Price — Selling Price Discount % = (Discount / Marked Price) × 100%
'Discount percentage is ALWAYS calculated on the MARKED PRICE, NOT on the selling price.'
Worked Example: A shopkeeper marks a shirt at Rs 600 and gives a discount of 15%. Find the SP.
Discount = 15% of 600 = 90 SP = 600 — 90 = Rs 510
Worked Example: After a discount of 12%, a book is sold for Rs 440. Find the marked price.
Let MP = M. M — 12% of M = M × 0.88 = 440 M = 440/0.88 = Rs 500
5. Profit When Discount is Given
Worked Example: A dealer marks an article at 25% above the CP and allows a discount of 10%. Find the profit percentage.
Let CP = Rs 100. MP = 100 + 25% of 100 = Rs 125. Discount = 10% of 125 = Rs 12.50. SP = 125 — 12.50 = Rs 112.50. Profit = 112.50 — 100 = Rs 12.50. Profit % = 12.50%
6. Successive Discounts
When two discounts d₁% and d₂% are given successively: Final SP = MP × (1 — d₁/100) × (1 — d₂/100)
Worked Example: Find the single discount equivalent to two successive discounts of 20% and 10%.
Let MP = 100. After first discount: 100 × 0.8 = 80. After second discount: 80 × 0.9 = 72. Total discount = 100 — 72 = 28%. Single equivalent discount = 28%.
'Two successive discounts of 20% and 10% do NOT equal 30%. The actual discount is 28%.'
Common Mistakes and Fixes
| Mistake | Fix |
|---|---|
| 'Profit % = (Profit/SP) × 100' | Profit % is ALWAYS calculated on CP |
| 'Discount % = (Discount/SP) × 100' | Discount % is ALWAYS calculated on MP |
| 'Overhead expenses are ignored' | OVERHEAD expenses are ADDED to CP |
| '10% + 20% discount = 30%' | Successive discounts are MULTIPLIED, not ADDED |
| 'Loss of 10% means SP = 90% of CP' | Correct! This formula IS valid |
ICSE Exam Focus (5–7 marks)
- 2-mark questions: Finding profit/loss percentage in simple cases
- 3-mark questions: Finding SP or CP when profit/loss % is given
- 4-mark questions: Discount and MP problems
- 6-mark questions: Multi-step problems with successive discounts and overhead expenses
Self-Test
Q1. A person buys an article for Rs 360 and sells it at a profit of 15%. Find the SP. A1. SP = (100 + 15)/100 × 360 = 115/100 × 360 = Rs 414.
Q2. By selling a bicycle for Rs 1650, a dealer loses 12%. Find the CP. A2. CP = 100/(100 — 12) × 1650 = 100/88 × 1650 = Rs 1875.
Q3. A shopkeeper marks a TV at Rs 24,000 and allows a discount of 8%. Find the SP. A3. Discount = 8% of 24000 = Rs 1920. SP = 24000 — 1920 = Rs 22,080.
Q4. A trader marks his goods 30% above CP and gives a discount of 15%. Find the profit percentage. A4. Let CP = 100. MP = 130. Discount = 15% of 130 = 19.5. SP = 110.5. Profit = 10.5%. Profit % = 10.5%.
Q5. The marked price of a shirt is Rs 500. It is sold at a discount of 20%. If the cost price is Rs 350, find the profit or loss percentage. A5. SP = 500 × 0.8 = Rs 400. CP = 350. Profit = 50. Profit % = (50/350) × 100 ≈ 14.29%.
Q6. Find the single discount equivalent to successive discounts of 15% and 10%. A6. Let MP = 100. After 15%: 85. After 10%: 85 × 0.9 = 76.5. Total discount = 23.5%. Single equivalent discount = 23.5%.
