Profit, Loss and Discount
Overview
Profit, Loss and Discount forms the backbone of commercial mathematics at the primary level. This topic connects classroom learning directly to everyday transactions—buying groceries, selling items at a fair, or understanding shop discounts during festivals. For JTET Paper I, questions test both computational accuracy and conceptual clarity about how these terms relate to each other.
Students must understand the relationship between Cost Price (CP), Selling Price (SP), Marked Price (MP), and how profit, loss and discount percentages are calculated. Questions typically involve straightforward calculations but require careful attention to which price serves as the base for percentage computation. Mastery here also builds foundation for simple interest and ratio-proportion problems.
Word problems dominate, requiring students to extract relevant data and apply the correct formula.
Key Concepts
- Cost Price (CP) is the price at which an item is bought or manufactured. All profit/loss calculations use CP as the base.
- Selling Price (SP) is the price at which an item is sold. Comparing SP with CP determines profit or loss.
- Profit occurs when SP > CP. The seller earns more than what was spent.
- Loss occurs when SP < CP. The seller receives less than what was spent.
- Marked Price (MP) is the price printed/labelled on an item before any discount. It is also called the list price or catalogue price.
- Discount is the reduction offered on MP. Discount is always calculated on MP, not on CP.
- Successive discounts are applied one after another on the reduced price, not on the original MP.
- Break-even means no profit, no loss—when SP exactly equals CP.
Formulas / Key Facts
| Concept | Formula |
|---|---|
| Profit | Profit = SP − CP |
| Loss | Loss = CP − SP |
| Profit Percentage | Profit % = (Profit / CP) × 100 |
| Loss Percentage | Loss % = (Loss / CP) × 100 |
| SP when Profit % is given | SP = CP × (100 + Profit%) / 100 |
| SP when Loss % is given | SP = CP × (100 − Loss%) / 100 |
| Discount | Discount = MP − SP |
| Discount Percentage | Discount % = (Discount / MP) × 100 |
| SP after Discount | SP = MP × (100 − Discount%) / 100 |
| Successive Discounts (a% and b%) | Net SP = MP × (100 − a)/100 × (100 − b)/100 |
Key facts to remember:
- Profit % and Loss % are always calculated on CP.
- Discount % is always calculated on MP.
- If two successive discounts of a% and b% are given, equivalent single discount = (a + b − ab/100)%.
Worked Examples
Example 1: Finding Profit and Profit Percentage
A shopkeeper buys a toy for ₹80 and sells it for ₹100. Find the profit and profit percentage.
Solution:
- CP = ₹80, SP = ₹100
- Profit = SP − CP = 100 − 80 = ₹20
- Profit % = (Profit / CP) × 100 = (20 / 80) × 100 = 25%
Answer: Profit = ₹20, Profit % = 25%
Example 2: Finding SP when Loss % is given
A book was bought for ₹150. It was sold at a loss of 10%. Find the selling price.
Solution:
- CP = ₹150, Loss % = 10%
- SP = CP × (100 − Loss%) / 100
- SP = 150 × (100 − 10) / 100 = 150 × 90 / 100 = ₹135
Answer: SP = ₹135
Example 3: Discount Calculation
A shirt has a marked price of ₹500. A discount of 20% is offered. Find the selling price and the discount amount.
Solution:
- MP = ₹500, Discount % = 20%
- Discount = MP × Discount% / 100 = 500 × 20 / 100 = ₹100
- SP = MP − Discount = 500 − 100 = ₹400
Answer: Discount = ₹100, SP = ₹400
Example 4: Successive Discounts
A watch has MP = ₹1000. Two successive discounts of 10% and 5% are given. Find the final SP.
Solution:
- After first discount (10%): Price = 1000 × 90/100 = ₹900
- After second discount (5%): SP = 900 × 95/100 = ₹855
Answer: Final SP = ₹855
Note: Two discounts of 10% and 5% are NOT equal to a single 15% discount. Single 15% discount would give SP = ₹850, which is less than ₹855.
Example 5: Finding CP when Profit % and SP are given
An item was sold for ₹540 at a profit of 8%. Find the cost price.
Solution:
- SP = CP × (100 + Profit%) / 100
- 540 = CP × 108 / 100
- CP = 540 × 100 / 108 = 54000 / 108 = ₹500
Answer: CP = ₹500
Common Mistakes
- Calculating profit/loss % on SP instead of CP → Always remember: Profit % and Loss % are on CP. The formula has CP in the denominator.
- Calculating discount % on CP instead of MP → Discount % is always computed on the marked price (MP), not on what the shopkeeper paid.
- Adding successive discounts directly → Two discounts of 10% and 10% do NOT equal 20%. Apply them sequentially: after first 10%, you get 90% of MP; then another 10% off that gives 81% of MP (equivalent to 19% total discount).
- Confusing MP with SP → MP is the labelled/sticker price before discount. SP is what the customer actually pays after discount.
- Ignoring the break-even condition → When SP = CP, there is neither profit nor loss. Students sometimes force a profit or loss calculation in such cases.
Quick Reference
- Profit = SP − CP; Loss = CP − SP
- Profit % and Loss % → base is always CP
- Discount % → base is always MP
- SP after discount = MP × (100 − Discount%) / 100
- Successive discounts multiply, don't add
- No profit, no loss when SP = CP