Profit, Loss and Discount

Profit, Loss and Discount — SSC CHSL Study Notes

Overview

This topic tests your ability to quickly calculate cost price (CP), selling price (SP), marked price (MP), profit/loss percentages, and discounts — often layered together in real-world transaction scenarios.

Students must master the relationships between these variables and develop mental shortcuts for percentage conversions. Questions typically involve shopkeepers buying and selling goods, applying successive discounts, or mixing profit/loss with markup/discount. Speed and accuracy are critical because these problems are computation-heavy but formulaic once you internalize the core patterns.

The topic integrates closely with percentage and ratio concepts. A strong grasp here also helps in Data Interpretation and real-life arithmetic reasoning sections.

Key Concepts

• Cost Price (CP) is the price at which an item is purchased or produced. All profit/loss calculations reference CP as the base.
• Selling Price (SP) is the price at which an item is sold to the customer. Profit or loss is determined by comparing SP to CP.
• Profit occurs when SP > CP. Profit = SP − CP. Profit percentage = (Profit / CP) × 100.
• Loss occurs when SP < CP. Loss = CP − SP. Loss percentage = (Loss / CP) × 100.
• Marked Price (MP) is the price tag displayed on an item before any discount. Shopkeepers typically mark up above CP to allow room for discounts while still making profit.
• Discount is the reduction offered on MP. Discount = MP − SP. Discount percentage is always calculated on MP, not CP.
• Successive discounts are multiple discounts applied one after another. They are not simply additive — each subsequent discount applies to the reduced price, not the original MP.
• The relationship chain is: CP → (markup) → MP → (discount) → SP. Profit or loss is always the difference between final SP and original CP.

Formulas / Key Facts

1. Profit = SP − CP; Profit % = (Profit / CP) × 100 = ((SP − CP) / CP) × 100
2. Loss = CP − SP; Loss % = (Loss / CP) × 100 = ((CP − SP) / CP) × 100
3. SP when profit % is given: SP = CP × (100 + Profit%) / 100
4. SP when loss % is given: SP = CP × (100 − Loss%) / 100
5. CP from SP and profit %: CP = SP × 100 / (100 + Profit%)
6. CP from SP and loss %: CP = SP × 100 / (100 − Loss%)
7. Marked Price and Discount: SP = MP × (100 − Discount%) / 100
8. Successive discounts d₁% and d₂%: Net discount % = d₁ + d₂ − (d₁ × d₂)/100 Final SP = MP × (100−d₁)/100 × (100−d₂)/100
9. Markup %: MP = CP × (100 + Markup%) / 100
10. Dishonest dealer with faulty weights: Effective profit % = (Error% / (True value − Error%)) × 100

Worked Examples

Example 1: Basic profit percentage A shopkeeper buys an article for ₹500 and sells it for ₹650. Find profit percentage. Solution: Profit = SP − CP = 650 − 500 = ₹150 Profit % = (150/500) × 100 = 30%

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Example 2: Finding CP from SP and loss percentage By selling an item at ₹720, a trader incurs a loss of 10%. What is the CP? Solution: SP = CP × (100 − Loss%)/100 720 = CP × 90/100 CP = (720 × 100)/90 = ₹800

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Example 3: Successive discounts An article with MP ₹2000 is sold at successive discounts of 20% and 10%. Find the final SP. Solution: After first 20% discount: SP₁ = 2000 × 80/100 = ₹1600 After second 10% discount: SP = 1600 × 90/100 = ₹1440 Alternatively using formula: Net discount % = 20 + 10 − (20×10)/100 = 30 − 2 = 28% SP = 2000 × 72/100 = ₹1440

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Example 4: Markup and discount to achieve target profit A shopkeeper marks an item 40% above CP and gives a 10% discount. If CP is ₹500, find SP and profit %. Solution: MP = 500 × 140/100 = ₹700 SP = 700 × 90/100 = ₹630 Profit = 630 − 500 = ₹130 Profit % = (130/500) × 100 = 26%

Common Mistakes

Mistake 1: Calculating discount percentage on CP instead of MP. Fix: Always remember discount % = (Discount/MP) × 100, not on CP. MP is the reference base for discount.

Mistake 2: Adding successive discounts directly (e.g., 20% + 10% = 30%). Fix: Use the formula: Net % = d₁ + d₂ − (d₁×d₂)/100. Successive discounts compound, they don't add linearly.

Mistake 3: Confusing profit % base with SP instead of CP. Fix: Profit % and Loss % are always calculated as a percentage of CP, never SP. The formula denominators always use CP.

Mistake 4: Applying markup on MP or discount on CP. Fix: Markup is applied to CP to get MP. Discount is applied to MP to get SP. Follow the chain: CP → MP → SP.

Mistake 5: Using wrong formula direction — e.g., finding CP from SP but using the SP-from-CP formula. Fix: When finding CP from SP, invert the multiplier. If SP = CP × (100+x)/100, then CP = SP × 100/(100+x).

Quick Reference

• Profit when SP > CP: Profit% = ((SP−CP)/CP) × 100
• Loss when SP < CP: Loss% = ((CP−SP)/CP) × 100
• SP from profit%: SP = CP(100+P%)/100; from loss%: SP = CP(100−L%)/100
• Successive discounts d₁, d₂: Net = d₁ + d₂ − d₁d₂/100
• Discount is on MP, Profit/Loss is on CP — never mix the bases
• Quick check: If MP = CP × 1.4 and discount = 10%, net profit = 40% − 10% (approx) = 26% (exact: use chain multiplication)