SSC CGL Preparation – Day 4

Quantitative Aptitude – PROFIT AND LOSS (Basic Level)

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🔶 1. BASIC TERMINOLOGIES

Term	Definition
Cost Price (CP)	The price at which an article is bought.
Selling Price (SP)	The price at which an article is sold.
Profit / Gain	When SP > CP → Profit = SP − CP
Loss	When CP > SP → Loss = CP − SP
Marked Price (MP)	The listed price before any discount.
Discount	The reduction offered on MP → Discount = MP − SP

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🔶 2. PROFIT & LOSS FORMULAS

Type	Formula
Profit %	$$Profit\%=(\frac{Profit}{CP}) \times 100$$
Loss %	$$Loss\%=(\frac{Loss}{CP}) \times 100$$
SP when profit % is given	$$\text{SP} = \text{CP} \left(1 + \frac{\text{Profit%}}{100} \right)$$
SP when loss % is given	$$\text{SP} = \text{CP} \left(1 – \frac{\text{Loss%}}{100} \right)$$
CP when SP and profit % are known	$$\text{CP} = \frac{\text{SP}}{1 + \frac{\text{Profit%}}{100}}$$
CP when SP and loss % are known	$$\text{CP} = \frac{\text{SP}}{1 – \frac{\text{Loss%}}{100}}$$​
Successive Profit/Loss	$$\text{Net %} = a + b + \frac{ab}{100}$$​ (where a and b are profit/loss percentages)
Discount %	$$\frac{\text{Discount}}{\text{Marked Price}} \times 100$$

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🔶 3. IMPORTANT CASES

✅ Case 1: No profit no loss

$$\text{SP} = \text{CP}$$

✅ Case 2: Selling at x% profit and y% loss

Use the formula: $$\text{Net %} = x + y + \frac{xy}{100}​$$

(If both profit or both loss) $$\text{Net %} = x – y – \frac{xy}{100}$$

(If one is profit, other is loss)

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🔶 4. SUCCESSIVE DISCOUNTS

If two successive discounts are given, say 20% and 10%, then: $$\text{Net Discount %} = 20 + 10 – \frac{20 \times 10}{100}$$

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🔶 5. SHORTCUTS

• If SP is x% more than CP → Profit % = x
• If SP is x% less than CP → Loss % = x
• If Profit % = Loss %, then % = 0 → No gain, no loss
• Always compare profit/loss % with respect to CP, not SP

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🔶 6. EXAMPLES

🧮 Example 1:

CP = ₹100, Profit = 20%, find SP

$$\text{SP} = 100 \times \left(1 + \frac{20}{100}\right) = ₹120$$

🧮 Example 2:

SP = ₹240, Loss = 20%, find CP

$$\text{CP} = \frac{240}{1 – \frac{20}{100}} = \frac{240}{0.8} = ₹300$$

🧮 Example 3:

Marked Price = ₹200, Discount = 10%, find SP

$$\text{SP} = 200 – \frac{10}{100} \times 200 = 200 – 20 = ₹180$$

🧮 Example 4:

Successive discounts of 20% and 10% on ₹500 $$\text{Net Discount %} = 20 + 10 – \frac{20 \times 10}{100} = 28\% \Rightarrow \text{SP} = 500 – 28\% \text{ of } 500 = ₹360$$

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🔶 7. SSC CGL TIPS

Don’t forget unitary method logic for compound selling (e.g., 3 for ₹10, sold at 2 for ₹9)

Most questions involve reverse calculation (e.g., finding CP or MP)

Master successive discount logic, often used in shops-type questions

Learn the profit/loss triangle: a fast tool to switch among SP, CP, and %