Profit, Loss and Discount — SSC CHSL Study Notes
Overview
Profit, Loss and Discount is a cornerstone of the SSC CHSL Quantitative Aptitude section, appearing in 2–4 questions every year. 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