Discount

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Discount is a reduction in the marked price (MP) of an article. It’s a concept frequently tested in SSC CGL Quantitative Aptitude, appearing in problems involving shopping, bills, and profit-loss calculations. Understanding discounts helps determine the final selling price after reductions.

Key Terms:

• Marked Price (MP): The original price listed on an article (also called List Price or Tag Price)
• Selling Price (SP): The actual price after discount is applied
• Discount: The reduction amount, usually given as a percentage

Core Formulas:

$$\text{Discount %} = \frac{\text{Discount}}{\text{Marked Price}} \times 100$$

$$\text{Selling Price} = \text{Marked Price} - \text{Discount}$$

$$\text{Selling Price} = \text{MP} \times \left(1 - \frac{d}{100}\right)$$

Where $d$ = discount percentage

⚡ SSC CGL Exam Tips:

• Discount is always calculated on Marked Price, never on Cost Price
• When multiple discounts are offered, apply them sequentially (NOT add them)
• Successive discounts of 20% and 10% is NOT 30% discount
• “25% off” means you pay 75% of the marked price

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Understanding Discount with Worked Examples

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

Discount = 15% of 800 = 0.15 × 800 = ₹120 Selling Price = 800 - 120 = ₹680

Or directly: SP = 800 × (1 - 0.15) = 800 × 0.85 = ₹680

Example 2: Finding Marked Price An article is sold for ₹560 after a 20% discount. Find its marked price.

Let MP = x SP = x × (1 - 20/100) = 0.8x 0.8x = 560 x = 560/0.8 = ₹700

Example 3: Finding Discount Percentage A refrigerator with MP of ₹25,000 is sold for ₹22,000. What is the discount %?

Discount = 25000 - 22000 = ₹3,000 Discount % = (3000/25000) × 100 = 12%

Successive Discounts (Very Important):

When multiple discounts are applied one after another:

Example: Two successive discounts of 20% and 10% are offered on an article with MP of ₹500.

First discount: 20% of 500 = ₹100 Price after 1st discount = 500 - 100 = ₹400

Second discount: 10% of 400 = ₹40 Final price = 400 - 40 = ₹360

Shortcut for Successive Discounts: $$SP = MP \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right) \times …$$

For 20% and 10%: $$SP = 500 \times 0.80 \times 0.90 = 500 \times 0.72 = ₹360$$

Equivalent Single Discount: For successive discounts of $d_1$% and $d_2$%: $$d_{eq} = d_1 + d_2 - \frac{d_1 \times d_2}{100}$$

For 20% and 10%: $$d_{eq} = 20 + 10 - \frac{20 \times 10}{100} = 30 - 2 = 28%$$

So 20% + 10% successive = 28% single discount (not 30%!)

Common Student Mistakes:

1. Adding discounts directly instead of applying successively
2. Confusing Cost Price with Marked Price
3. Forgetting that discount is calculated on MP, not on any other price
4. Misinterpreting “double discount” (means 2 discounts, not 2× discount)

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage with profit-loss connections and previous year SSC CGL patterns.

Relationship Between Discount and Profit-Loss:

Given	To Find	Formula
CP, Discount %	Profit/Loss %	Find SP from MP and discount, then compare with CP
SP, Discount %	MP	MP = SP / (1 - d/100)
MP, SP	Discount %	Discount = (MP - SP)/MP × 100

Example: Profit-Loss with Discount A trader offers 20% discount on MP and still makes 10% profit. If CP = ₹900, find MP and SP.

Solution: Let MP = x SP after 20% discount = 0.8x Profit = 10% on CP = 0.1 × 900 = ₹90 SP = CP + Profit = 900 + 90 = ₹990 0.8x = 990 x = 990/0.8 = ₹1,237.50

Special Discount Scenarios:

Scenario 1: Discount at two stages with a markup in between A retailer buys at 20% discount on MP and sells at marked price. What is profit %?

Let MP = 100 Cost = 80 (20% discount on MP) Selling = 100 (at MP) Profit = 100 - 80 = 20 Profit % = (20/80) × 100 = 25%

Scenario 2: “Trade Discount” vs “Cash Discount”

• Trade discount: Given to traders (regular business purchases)
• Cash discount: Given for prompt payment (like 2% for cash payment within a week) Trade discount is calculated on MP first, then cash discount on the resulting price.

Previous Year SSC CGL Patterns:

SSC CGL 2022 Question: The marked price of an article is ₹1,200. It is sold at a discount of 15%. If the shopkeeper still makes a profit of 20%, and his cost price is ₹800, find the actual profit earned.

Solution: MP = 1200, Discount = 15% SP = 1200 × 0.85 = ₹1,020 CP = 800 Profit = 1020 - 800 = ₹220 Profit % = (220/800) × 100 = 27.5%

SSC CGL 2023 Question: The price of an article is reduced by 20% first, then by 10% of the new price. If the final price is ₹720, find the original price.

Solution: Let original price = x After 20% reduction: 0.8x After additional 10% reduction: 0.9 × 0.8x = 0.72x 0.72x = 720 x = 720/0.72 = ₹1,000

SSC CGL 2023 Question: What single discount equals three successive discounts of 10%, 15%, and 20%?

Solution: $$d_{eq} = 1 - (1-0.10)(1-0.15)(1-0.20)$$ $$= 1 - (0.90 \times 0.85 \times 0.80)$$ $$= 1 - 0.612 = 0.388 = 38.8%$$

Advanced Applications:

• Discount graphs and break-even analysis
• Inverse problem: Finding original price when only final price and discount% are known
• Maximum discount a retailer can offer while still covering costs
• “Chain discounts” in wholesale pricing

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