Quantitative Aptitude
Number System Percentage Profit, Loss & Discount Time & Work Speed, Distance & Time Simple & Compound Interest Ratio, Proportion & Mixture Mensuration Data Interpretation
Module 2 · IBPS PO Quantitative Aptitude

Percentage

Percentage change, successive percentages, population problems.
Basic % · Successive Change · Election Problems
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Learning Objectives

  • Understand the fundamental concepts of Percentage
  • Apply key formulas and techniques to solve problems
  • Practice with exam-level questions to build speed and accuracy

Key Concepts

What is Percentage?

Percentage means "per hundred" (parts out of 100). It is one of the most important topics in SSC CGL Tier 1 quant section, forming the basis for profit-loss, simple interest, and data interpretation questions.

Key Concepts

1. Basic Formula: Percentage = (Part / Whole) * 100. To convert a fraction to a percentage, multiply by 100. To convert a percentage to a fraction, divide by 100.

2. Fraction-Percentage Equivalents: Memorise these: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/7 = 14.28%, 1/8 = 12.5%, 1/9 = 11.11%, 1/10 = 10%, 1/11 = 9.09%, 1/12 = 8.33%.

3. Percentage Change: If a value increases from A to B, % increase = ((B-A)/A) * 100. If it decreases, % decrease = ((A-B)/A) * 100.

4. Successive Percentage Change: If a number is changed by x% and then by y%, net change = x + y + (xy/100)%. A single discount equivalent to two successive discounts of x% and y% is: x + y - (xy/100).

Solved Examples

Example 1 (Basic)
What is 12.5% of 640?

a) 60 b) 70 c) 80 d) 90
Solution: c) 80. 12.5% = 1/8. So 1/8 of 640 = 640 / 8 = 80.
Example 2 (Successive Change)
A number is first increased by 10% and then decreased by 10%. What is the net percentage change?

a) 0% b) 1% increase c) 1% decrease d) 2% decrease
Solution: c) 1% decrease. Net change = 10 + (-10) + (10*(-10))/100 = 0 - 1 = -1%.
Example 3 (Election)
In an election, candidate A got 60% of the total valid votes. If total votes were 50,000 and 10% of votes were invalid, how many valid votes did A get?

a) 24,000 b) 27,000 c) 30,000 d) 32,000
Solution: b) 27,000. Valid votes = 50,000 * 90% = 45,000. A votes = 60% of 45,000 = 27,000.

Shortcut Techniques

  • Use fraction equivalents instead of decimals for faster mental math. 12.5% = 1/8, 33.33% = 1/3.
  • For "x% of y = y% of x" — always switch to the easier side. 8% of 25 = 25% of 8 = 2.
  • For successive discounts, apply the formula directly rather than calculating step by step.
  • In population increase/decrease questions, multiply by factors: 10% increase = multiply by 1.1, 10% decrease = multiply by 0.9.
Pro Tip: For SSC CGL, mastering fraction-percentage equivalents up to 1/20 saves 30-40 seconds per question. Practice converting fractions to percentages in your head instantly.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Practice Questions

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