SSC CGL Preparation – Day 12

Quantitative Aptitude: Profit and Loss – Revision + Advanced Concepts

🔁 Quick Recap of Basics

• Cost Price (CP): The price at which an article is purchased.
• Selling Price (SP): The price at which the article is sold.
• Profit (Gain): When SP > CP
  → Profit = SP – CP
• Loss: When CP > SP
  → Loss = CP – SP
• Profit% = (Profit/CP) × 100
• Loss% = (Loss/CP) × 100
• SP (when profit) = CP × (100 + Profit%)/100
• SP (when loss) = CP × (100 – Loss%)/100
• CP (when profit) = SP × 100/(100 + Profit%)
• CP (when loss) = SP × 100/(100 – Loss%)

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💡 Important Advanced Concepts

1. Successive Profit and Loss:

If two successive profit percentages are given (say x% and y%), use the formula: $$\text{Net% Gain/Loss} = x + y + \frac{xy}{100}$$

If result is negative, it’s a loss.

2. Discount and Marked Price:

• Marked Price (MP): The price written/tagged on the article.
• Discount: Reduction offered on MP.
• Selling Price = MP – Discount
• When multiple discounts are given:

$$\text{Net Discount%} = x + y – \frac{xy}{100}$$

3. False Weights:

When shopkeepers cheat using false weights: $$\text{Gain%} = \left( \frac{\text{True Weight} – \text{False Weight}}{\text{False Weight}} \right) \times 100$$

4. Marked Price and Profit Relationship:

If profit is calculated on CP and discount on MP: $$MP = \frac{(CP)}{(100 – Discount/%)} × (100 + Profit/%) / 100$$

5. Trader Mixing Costly and Cheap Products:

To find profit % when a trader mixes 2 types and sells at average SP:
Use Alligation Method.

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🧮 Sample SSC-Oriented Problems

Example 1:
An article is bought for ₹200 and sold for ₹240. Find the profit %.

Solution:
Profit = 240 – 200 = ₹40
Profit% = (40/200) × 100 = 20%

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Example 2:
Marked Price of a book is ₹500. A shopkeeper offers 10% discount and still earns 20% profit. Find CP.

Solution:
SP = MP – Discount = 500 – 10% of 500 = ₹450
Let CP = x
Then, Profit% = (450 – x)/x × 100 = 20%
450 = 1.2x → x = 450 / 1.2 = ₹375

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Example 3:
A dishonest dealer professes to sell at cost price but uses 950g instead of 1kg. Find his gain%.

Solution:
Gain% = (1000 – 950)/950 × 100 = 5.26%

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Example 4:
An item is marked at ₹800. After two successive discounts of 10% and 5%, what is the final price?

Solution:
After 10% discount → 800 – 80 = ₹720
Then 5% discount on 720 → 720 – 36 = ₹684
Final Price = ₹684

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⚠️ Common Traps in SSC CGL

• Applying discount on CP instead of MP.
• Confusing Profit% and Loss% base (always CP unless stated).
• Forgetting to apply successive discount formula properly.

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📝 Pro Tips for SSC CGL

1. Use ratio approach when CP and SP are in ratio.
2. For quick successive % changes, memorize the net % formula.
3. Practice questions involving combinations: Marked Price, Discounts, and Profit together.
4. Watch for units in false weight questions (grams, kg).