Discount — Study Notes

Overview

Discount is a reduction in the marked price (list price) of an item. In SSC GD examinations, discount problems appear regularly in the Elementary Mathematics section, typically testing your ability to calculate the selling price after applying single or successive discounts, or to work backwards from given conditions to find the original marked price or discount percentage.

Understanding discount is critical because it connects directly with profit and loss, percentage calculations, and real-world pricing scenarios. Questions may involve straightforward single discount calculations or require multiple-step reasoning for successive discounts. The key skill is recognizing that discounts always apply to the marked price (not cost price), and that successive discounts cannot simply be added—they must be applied sequentially. Mastering this 2–3 mark topic will boost your speed and accuracy in the Mathematics section.

Most SSC GD questions on discount are direct formula-based problems or two-step word problems. You must be comfortable converting percentages to fractions, applying discount formulas quickly, and understanding the relationship between marked price, discount, and selling price.

Key Concepts

• **Marked Price (MP)**: The printed or listed price of an item before any discount is applied. Also called List Price or Tag Price.

• **Discount**: The reduction offered on the marked price, usually expressed as a percentage of the marked price. Discount = MP − SP.

• **Selling Price (SP)**: The actual price at which the item is sold to the customer after applying the discount. SP = MP − Discount.

• **Single Discount**: A one-time percentage reduction on the marked price. If discount is d%, then SP = MP × (100 − d)/100.

• **Successive Discounts**: Two or more discounts applied one after another. Each subsequent discount is calculated on the price remaining after the previous discount, not on the original marked price.

• **Equivalent Single Discount**: When two successive discounts d₁% and d₂% are applied, the net effect is equivalent to a single discount of [d₁ + d₂ − (d₁ × d₂)/100]%.

• **Discount and Profit/Loss**: Discount is given on marked price; profit or loss is calculated on cost price. A shopkeeper may mark up an item above cost price, then offer a discount on that marked price and still make a profit.

Formulas / Key Facts

1. **Selling Price after Single Discount**: SP = MP × (100 − d)/100 where d is the discount percentage.

2. **Discount Amount**: Discount = MP × d/100 or Discount = MP − SP.

3. **Marked Price from SP and Discount**: MP = SP × 100/(100 − d) or MP = (100 × SP)/(100 − d).

4. **Discount Percentage**: Discount% = (Discount/MP) × 100 or Discount% = [(MP − SP)/MP] × 100.

5. **Successive Discounts Formula**: For two discounts d₁% and d₂%, the equivalent single discount is: D = d₁ + d₂ − (d₁ × d₂)/100. Then SP = MP × (100 − D)/100.

6. **Selling Price after Two Successive Discounts (Direct)**: SP = MP × (100 − d₁)/100 × (100 − d₂)/100.

7. **Three Successive Discounts**: SP = MP × (100 − d₁)/100 × (100 − d₂)/100 × (100 − d₃)/100.

8. **Relation with Profit**: If an item is marked at x% above cost price (CP) and a discount d% is given: SP = CP × (100 + x)/100 × (100 − d)/100.

Worked Examples

**Example 1**: A shirt has a marked price of ₹800. A discount of 15% is offered. Find the selling price.

**Solution**: MP = ₹800, d = 15% SP = MP × (100 − d)/100 SP = 800 × (100 − 15)/100 = 800 × 85/100 = 800 × 0.85 = ₹680 **Answer**: ₹680

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**Example 2**: A shopkeeper offers two successive discounts of 20% and 10% on a television marked at ₹15,000. What is the final selling price?

**Solution**: MP = ₹15,000, d₁ = 20%, d₂ = 10% Method 1 (step-by-step): After first discount: SP₁ = 15000 × (100 − 20)/100 = 15000 × 80/100 = ₹12,000 After second discount: SP = 12000 × (100 − 10)/100 = 12000 × 90/100 = ₹10,800 Method 2 (equivalent single discount): D = 20 + 10 − (20 × 10)/100 = 30 − 2 = 28% SP = 15000 × (100 − 28)/100 = 15000 × 72/100 = ₹10,800 **Answer**: ₹10,800

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**Example 3**: After allowing a discount of 12% on the marked price, a shopkeeper still makes a profit of 10%. If the cost price is ₹1,000, what is the marked price?

**Solution**: Let MP be the marked price. SP = MP × (100 − 12)/100 = MP × 88/100 = 0.88 × MP Profit = 10%, so SP = CP × (100 + 10)/100 = 1000 × 110/100 = ₹1,100 Therefore, 0.88 × MP = 1100 MP = 1100/0.88 = ₹1,250 **Answer**: ₹1,250

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**Example 4**: Two successive discounts of 25% and 20% are equivalent to what single discount?

**Solution**: d₁ = 25%, d₂ = 20% Equivalent single discount D = 25 + 20 − (25 × 20)/100 = 45 − 5 = 40% **Answer**: 40%

Common Mistakes

1. **Adding successive discounts directly**: Students often add 20% + 10% = 30% for successive discounts. Wrong! Successive discounts apply sequentially, so you must multiply the remaining percentages: (100 − 20)/100 × (100 − 10)/100. The correct equivalent single discount is 28%, not 30%.

2. **Applying discount on cost price instead of marked price**: Discount is always calculated on the marked price (list price), not the cost price. If a question mentions both CP and discount, first determine the marked price, then apply the discount.

3. **Confusing discount amount with discount percentage**: Discount percentage is always calculated as (Discount/MP) × 100. If you're given a discount amount, divide it by the marked price and multiply by 100 to get the percentage—don't assume the absolute discount is the percentage.

4. **Forgetting to convert percentage to decimal in calculations**: When using formulas, remember that d% means d/100. Writing SP = MP × (100 − d) without dividing by 100 is a common arithmetic slip. Always include the /100 factor.

5. **Reversing the order in backward calculations**: When finding marked price from selling price and discount, use MP = (100 × SP)/(100 − d), not MP = SP × (100 − d)/100. The latter gives you a smaller number, not the original larger marked price.

Quick Reference

• **SP = MP − Discount** or **SP = MP × (100 − d)/100** for single discount d%.
• **Two successive discounts d₁% and d₂% = single discount of [d₁ + d₂ − (d₁ × d₂)/100]%**.
• **Discount is always on marked price, profit/loss is always on cost price**.
• For quick mental math: 10% discount → multiply by 0.9; 20% → multiply by 0.8; 25% → multiply by 0.75.
• **Successive discounts cannot be added; always apply step-by-step or use the formula**.
• If MP is x% above CP and discount is d%, then **SP = CP × (100 + x)/100 × (100 − d)/100**.