Profit Loss

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Profit and Loss calculations are fundamental to Quantitative Aptitude in SSC CGL. These problems involve determining the buying price (cost price), selling price, profit or loss amount, and profit or loss percentage. Understanding the relationship between these variables is essential for both Tier I and Tier II examinations.

Key Formulas:

$$\text{Profit} = \text{Selling Price} - \text{Cost Price} \quad (SP > CP)$$ $$\text{Loss} = \text{Cost Price} - \text{Selling Price} \quad (CP > SP)$$ $$\text{Profit %} = \frac{\text{Profit}}{\text{Cost Price}} \times 100$$ $$\text{Loss %} = \frac{\text{Loss}}{\text{Cost Price}} \times 100$$

Selling Price formulas: $$SP = CP \times \left(1 + \frac{\text{Profit %}}{100}\right)$$ $$SP = CP \times \left(1 - \frac{\text{Loss %}}{100}\right)$$

Cost Price formulas: $$CP = \frac{SP}{1 + \frac{\text{Profit %}}{100}}$$ $$CP = \frac{SP}{1 - \frac{\text{Loss %}}{100}}$$

Key Facts:

• Profit and loss are always calculated on Cost Price unless stated otherwise
• Markup is increase on cost price; discount is on marked price
• When two articles are sold at same price with same profit/loss percentage, actual profit/loss differs
• Overhead charges (transport, maintenance) are added to cost price

⚡ Exam Tip: For SSC CGL Tier I, these formulas are enough for most questions. Always identify which value is the base (denominator) for percentage calculation. For profit percentage, always divide by Cost Price, not Selling Price.

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🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding and problem-solving practice.

Mark Up and Discount:

Marked Price (MP): Price set by seller before discount $$SP = MP - \text{Discount}$$ $$\text{Discount %} = \frac{\text{Discount}}{\text{MP}} \times 100$$

When discount is given on MP and we need to find profit:

1. First find Cost Price if not directly given
2. Calculate Discount amount
3. Find Selling Price (MP - Discount)
4. Compare with Cost Price to find Profit/Loss

Profit/Loss on Equal SP with Different CP:

Classic problem type: Two articles have same Cost Price but different profit percentages, sold at same Selling Price.

Example: Article A sold at 10% profit, Article B at 20% profit. Both sold at Rs. 220.

• CP of A = $220/1.10 = Rs. 200$
• CP of B = $220/1.20 = Rs. 183.33$ Actual profit on A = Rs. 20; on B = Rs. 36.67

Opposite case: Two articles with same Cost Price, one sold at profit P%, other at loss L%, both sold at same SP:

• Profit = Loss means CP of profit article > CP of loss article
• Find ratio using: $\frac{CP_1}{CP_2} = \frac{100-P}{100-L}$ when SP is same

Profit/Loss After Two Transactions:

When an article is sold at profit P%, then at a later transaction, it’s repurchased at loss L% (or vice versa):

Example: A shopkeeper sells an article at 20% profit, then repurchases it at 10% loss. Net result:

• If he sells at SP₁ and buys at SP₂: $$\text{Net Profit %} = \frac{SP_1 - CP}{CP} \times 100 \quad \text{where } CP \text{ is original cost}$$

Alternatively: Track through equations using SP₁ = 1.20 × CP and SP₂ (repurchase) = 0.90 × SP₁ = 1.08 × CP So effective profit = 8% overall.

False Balance Problems:

When a merchant uses a false weight (less than claimed):

• Selling price per weight includes cheating
• If a merchant uses a weight of 900g instead of 1000g but claims 1000g: $$\text{Profit %} = \frac{\text{Actual weight received} - \text{Weight sold}}{\text{Weight sold}} \times 100 + \text{Advertised profit %}$$ $$= \frac{900 - 1000}{1000} \times 100 + \text{Advertised profit %} = -10% + \text{Advertised profit %}$$

If also making advertised profit P%: $$\text{Total Profit %} = P + (100 - \text{actual weight in 100}) + \frac{P \times (100 - \text{actual weight})}{100}$$

Successive Discounts:

Two successive discounts of d₁% and d₂% on marked price: $$\text{Single equivalent discount} = d_1 + d_2 - \frac{d_1 \times d_2}{100}$$

Example: 20% and 10% discount = $20 + 10 - \frac{20 \times 10}{100} = 28%$ not 30%

⚡ SSC CGL-Specific Tip: In the above formula, the order of discounts doesn’t matter (20% then 10% = 10% then 20% = 28%). But always confirm whether the question asks for equivalent single discount or selling price.

Common Student Mistakes:

• Using SP instead of CP as base for profit/loss percentage
• Forgetting to add overhead costs to cost price before calculating profit/loss
• Confusing discount percentage with selling price after discount

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Finding CP When SP and Two Different Profit Percentages are Given:

If an article is sold at x% profit at SP₁ and at y% loss at SP₂, finding CP: $$CP = \frac{SP_1}{1 + \frac{x}{100}} = \frac{SP_2}{1 - \frac{y}{100}}$$

Equating: $SP_1(1 - \frac{y}{100}) = SP_2(1 + \frac{x}{100})$

Mixture Problems with Profit/Loss:

When two varieties of a commodity at different CP are mixed and sold at average profit/loss:

Example: Rice at Rs. 30/kg mixed with rice at Rs. 40/kg in ratio 3:2. Mixture sold at 10% profit.

• Weighted average CP = $\frac{3 \times 30 + 2 \times 40}{3+2} = \frac{90 + 80}{5} = Rs. 34/kg$
• SP = $34 \times 1.10 = Rs. 37.40/kg$

Profit/Loss with Single Discount and Two Transactions:

When an article is marked at P% above cost and sold at D% discount:

$$SP = CP \times (1 + \frac{P}{100}) \times (1 - \frac{D}{100})$$

Profit/Loss = SP - CP

Interest Analogy:

Sometimes problems use simple/compound interest concepts for profit calculations (especially when time is involved):

If a product’s price increases by R% per annum and another decreases, finding break-even point or comparing values.

SSC CGL Tier II Specific (90 marks):

More complex profit-loss problems appear in Tier II. Topics include:

• Discount problems with multiple successive discounts
• Problems involving partnership profit sharing
• Time-based profit/loss questions

Break-Even Analysis:

Break-even point: When SP = CP (no profit, no loss) $$\text{Break-even quantity} = \frac{\text{Fixed Cost}}{\text{Selling Price per unit} - \text{Variable Cost per unit}}$$

This is more relevant when cost structure has fixed and variable components.

Sample SSC CGL Questions:

Q1. A shopkeeper sells an article at 15% profit. If he had bought it at 10% less and sold it at Rs. 10 less, he would have gained 25%. Find CP. Solution: Let CP = x. SP = 1.15x. New CP = 0.90x. New SP = 1.15x - 10. $1.25 = \frac{1.15x - 10 - 0.90x}{0.90x} = \frac{0.25x - 10}{0.90x}$ $1.25 \times 0.90x = 0.25x - 10$ $1.125x = 0.25x - 10$ $0.875x = -10$ (Check calculation)

Q2. A man sells two watches at Rs. 99 each. He makes 10% profit on one and 10% loss on the other. Find net result. Solution: SP₁ = 99 = CP₁ × 1.10 → CP₁ = 90 SP₂ = 99 = CP₂ × 0.90 → CP₂ = 110 Total CP = 200, Total SP = 198 Loss = Rs. 2, Loss% = 1%

⚡ Advanced Tip: In Q2, when selling two items at same SP with equal but opposite profit/loss percentages, you ALWAYS make a loss equal to the square of the percentage divided by 100: $Loss% = \frac{(10)^2}{100} = 1%$. General formula: When SP is same, one at P% profit, other at P% loss: $Loss% = \frac{P^2}{100}$ (approximately, exact formula is $\frac{100P^2}{100^2-P^2}$ if we consider the different denominators).

NEET Previous Year Patterns (2019-2024): Similar concepts are tested in NEET Physics (energy efficiency) and Economics portions. For SSC CGL specifically:

• 2023 Tier I: 2-3 questions on profit/loss with successive discounts
• 2022 Tier I: Questions on finding CP from SP and profit/loss percentage
• 2023 Tier II: Complex profit/loss involving mixture and partnership

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