SSC CGL Preparation – Day 17

Quantitative Aptitude – Percentage (Repeated)

✅ 1. Basic Definition

A percentage is a number or ratio expressed as a fraction of 100.
Symbol: % $$\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100$$

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✅ 2. Essential Conversions

Fraction	Percentage
1/2	50%
1/3	33.33%
1/4	25%
1/5	20%
1/6	16.66%
1/8	12.5%
1/9	11.11%
1/10	10%
2/3	66.66%
3/4	75%

👉 Learn these conversions thoroughly — they save a lot of time during exams.

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✅ 3. Key Formulae

1. To convert fraction to percentage:

$$\frac{a}{b} \times 100 = \text{Percentage}$$

2. To convert percentage to fraction:

$$x\% = \frac{x}{100}$$

3. % Increase or Decrease:

$$\text{Change \%} = \left( \frac{\text{Change}}{\text{Original}} \right) \times 100$$

4. If A is x% more/less than B, then B is:

$$\text{B} = A \times \frac{100}{100 \pm x}$$

5. Successive percentage change:

$$\text{Net \% change} = a + b + \frac{ab}{100}$$

(for two successive % changes a% and b%)

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✅ 4. Types of Questions in SSC CGL

🔹 Type A: Basic Conversion & Value-Based Questions

“What is 25% of 360?”
“What % is 36 out of 120?”

🔹 Type B: % Increase/Decrease

“If price of sugar is increased by 25%, by what % should consumption be decreased to keep expenditure constant?”

Formula used: $$\text{Required decrease} = \frac{x}{100 + x} \times 100$$

🔹 Type C: Population/Bacteria Growth

• Growth every year by x%:

$$\text{Population after n years} = P \left(1 + \frac{r}{100} \right)^n$$

• Decrease formula:

$$P \left(1 – \frac{r}{100} \right)^n$$

🔹 Type D: Income, Salary, Expenditure Problems

“If salary increases by 20% and expenditure increases by 10%, what is the % change in savings?”

$$\text{New saving} = \text{New income} – \text{New expenditure}$$

🔹 Type E: Percentage Comparisons Between Two Quantities

“A is 25% more than B. What % is B less than A?”

$$\text{Required \%} = \frac{\text{Difference}}{\text{Greater}} \times 100$$

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✅ 5. Shortcut Tricks

1. x% of y = y% of x
   E.g., 36% of 25 = 25% of 36
2. If A is x% more than B, then B is less than A by:

$$\frac{x}{100 + x} \times 100 \%$$

3. If A is x% less than B, then B is more than A by:

$$\frac{x}{100 – x} \times 100 \%$$

4. Successive % Increase/Decrease:
   e.g., increase by 20% then decrease by 10%
   Use:

$$\text{Net} = 20 + (−10) + \frac{20×(−10)}{100} = 10 − 2 = 8$$

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✅ 6. Examples

🔸 Q1: What is 35% of 240?

Solution:
= $$\frac{35}{100} \times 240 = 84$$

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🔸 Q2: Price of a shirt increased by 25%. By what % should it be reduced to bring it back to original price?

Solution:
Required % = $$\frac{25}{125} \times 100 = 20\%$$

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🔸 Q3: If population of a town increases by 10% annually, what will be the population after 2 years if current population is 10,000?

Solution: $$= 10000 \times \left(1 + \frac{10}{100} \right)^2 = 10000 \times 1.21 = 12100$$

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🔸 Q4: A number is increased by 20% and then decreased by 10%. What is the net change?

Solution:
Use:
20 − 10 − (20×10)/100 = 10 − 2 = 8% increase

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🔸 Q5: A’s income is 25% more than B’s. What % is B’s income less than A’s?

Solution:
Required % = $$\frac{25}{125} \times 100 = 20\%$$

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📌 Tips for SSC CGL

• Focus on % change logic, especially reverse % and successive % formulas.
• Practice shortcut tricks for income, salary, and population questions.
• Learn square roots and cubes for faster calculation in compound percentage-type questions.