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    Percentage

    Comprehensive study notes for SSC CGL preparation covering key concepts, important facts, previous year question analysis, and practice MCQs.

    Overview

    Percentage is one of the most versatile and high-frequency topics in the **SSC CGL** Quantitative Aptitude section. It appears both as standalone questions (2-3 per shift) and as a building block for Profit & Loss, Simple/Compound Interest, Data Interpretation, and Ratio & Proportion questions. Mastering percentages is non-negotiable for SSC CGL success. The SSC CGL Tier 1 Quantitative Aptitude section has **25 questions for 50 marks**. Percentage-based questions (direct + indirect) can account for **5-8 questions** across all topics. Understanding fraction-percentage equivalents and quick calculation tricks can save significant time.

    Key Concepts

    ### What is Percentage? Percentage means "per hundred" (from Latin "per centum"). It represents a fraction with denominator 100. - x% = x/100 - To convert fraction to percentage: multiply by 100 - To convert percentage to fraction: divide by 100 ### Basic Percentage Formulas 1. **Percentage of a number**: x% of N = (x/100) × N 2. **What percentage is A of B**: (A/B) × 100% 3. **Percentage increase**: [(New - Old)/Old] × 100% 4. **Percentage decrease**: [(Old - New)/Old] × 100% 5. **New value after x% increase**: N × (1 + x/100) 6. **New value after x% decrease**: N × (1 - x/100)

    Detailed Explanation

    ### Fraction-Percentage Equivalents (MUST MEMORIZE for SSC CGL) | Fraction | Percentage | Fraction | Percentage | |---|---|---|---| | 1/2 | 50% | 1/8 | 12.5% | | 1/3 | 33.33% | 1/9 | 11.11% | | 1/4 | 25% | 1/10 | 10% | | 1/5 | 20% | 1/11 | 9.09% | | 1/6 | 16.67% | 1/12 | 8.33% | | 1/7 | 14.28% | 2/3 | 66.67% | | 3/4 | 75% | 2/5 | 40% | | 3/5 | 60% | 4/5 | 80% | ### Successive Percentage Change When two successive changes of a% and b% are applied: **Net effect** = a + b + (ab/100) % **Example**: Price increases by 20% then decreases by 10%. Net effect = 20 + (-10) + (20 × (-10))/100 = 20 - 10 - 2 = **8% increase** ### Population/Depreciation Problems **Population after n years** (growth rate r%): P_final = P_initial × (1 + r/100)ⁿ **Value after depreciation** (rate r%): V_final = V_initial × (1 - r/100)ⁿ ### Percentage Change When Base Changes If A is x% more than B, then B is NOT x% less than A. **Formula**: If A is x% more than B, then B is [x/(100+x)] × 100% less than A. **Example**: If A is 25% more than B, then B is less than A by: [25/(100+25)] × 100 = [25/125] × 100 = **20%** ### Multiplier Method (Fastest for SSC CGL) Instead of calculating percentages step by step, use multipliers: - 10% increase → multiply by 1.1 - 20% decrease → multiply by 0.8 - 15% increase → multiply by 1.15 **Example**: A salary of Rs. 40,000 increases by 15% then decreases by 10%. = 40,000 × 1.15 × 0.90 = 40,000 × 1.035 = **Rs. 41,400**

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    Important Facts & Formulas

    ### Quick Calculation Tricks **Finding x% of a number:** - 10% of N = N/10 - 5% of N = N/20 (half of 10%) - 1% of N = N/100 - 15% of N = 10% + 5% = N/10 + N/20 - 25% of N = N/4 - 33.33% of N = N/3 - 12.5% of N = N/8 ### Percentage-Fraction Quick Convert Table | Percentage | Multiply by | Example: 240 | |---|---|---| | 10% | ÷10 | 24 | | 20% | ÷5 | 48 | | 25% | ÷4 | 60 | | 30% | ×3÷10 | 72 | | 33.33% | ÷3 | 80 | | 40% | ×2÷5 | 96 | | 50% | ÷2 | 120 | | 75% | ×3÷4 | 180 | ### Key Results to Remember - If a number increases by x% and then decreases by x%, the net result is always a **decrease** of (x²/100)% - If price increases by x%, consumption must decrease by [x/(100+x)] × 100% to keep expenditure same - If price decreases by x%, consumption must increase by [x/(100-x)] × 100% to keep expenditure same

    Previous Year Question Analysis

    ### SSC CGL Exam Trends (2019-2024) - Direct percentage: 2-3 questions per shift - Percentage in DI: 2-3 questions per shift - Successive percentage: At least 1 question per shift - Population/depreciation: Occasional (once in 2-3 shifts) ### Most Common Question Types 1. Finding percentage increase/decrease between two values 2. Successive percentage changes 3. "What percentage is A of B" type 4. Expenditure problems (price × consumption) 5. Election/examination pass-fail problems

    Practice MCQs (5 Questions with Answers)

    **Q1.** If the price of sugar increases by 25%, by what percentage should a household reduce consumption so that expenditure remains the same? (a) 25% (b) 20% (c) 30% (d) 15% **Answer: (b) 20%** Explanation: Reduction = [25/(100+25)] × 100 = [25/125] × 100 = 20%. **Q2.** A number is first increased by 20% and then decreased by 20%. The net change is: (a) 0% (b) 4% decrease (c) 4% increase (d) 2% decrease **Answer: (b) 4% decrease** Explanation: Net = 20 + (-20) + (20×(-20))/100 = 0 - 4 = -4%. Or: (x²/100)% = 400/100 = 4% decrease. **Q3.** In an election, candidate A gets 60% of votes. If 2% of votes are invalid and total votes are 10,000, how many valid votes did candidate A get? (a) 5880 (b) 6000 (c) 5800 (d) 5900 **Answer: (a) 5880** Explanation: Valid votes = 98% of 10,000 = 9,800. A's votes = 60% of 9,800 = 5,880. **Q4.** The population of a town is 50,000. It increases by 10% in the first year and 20% in the second year. Population after 2 years is: (a) 66,000 (b) 65,000 (c) 64,000 (d) 60,000 **Answer: (a) 66,000** Explanation: 50,000 × 1.10 × 1.20 = 50,000 × 1.32 = 66,000. **Q5.** If A's salary is 30% less than B's salary, then B's salary is what percent more than A's? (a) 30% (b) 42.85% (c) 35% (d) 40% **Answer: (b) 42.85%** Explanation: If A is 30% less than B, then B is more than A by [30/(100-30)] × 100 = [30/70] × 100 = 42.85%.

    Memory Tips & Mnemonics

    ### The "Fraction Friends" - Memorize These Pairs Think of fractions and percentages as friends that always go together: - **1/2 = 50%** (Half is always 50) - **1/3 ≈ 33%** and **2/3 ≈ 67%** (Thirds split into 33-67) - **1/4 = 25%** and **3/4 = 75%** (Quarters split into 25-75) - **1/5 = 20%** (Five fingers = 20%) - **1/8 = 12.5%** (Half of quarter) ### Successive Change Formula: "Add, Add, Multiply-Divide" For a% followed by b%: **a + b + ab/100** - First: Add the two percentages - Then: Add their product divided by 100 ### The Expenditure Triangle **Price × Consumption = Expenditure** If one goes up, the other must come down proportionally. Formula: "What goes UP by x, comes DOWN by x/(100+x)"