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Percentage Word Problems

UP Police Constable · Quantitative Aptitude

Also prepare for:CRPF Const BSF Const CISF Const ITBP Const

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Core Concept

Read this first — the foundation of the topic

→Core Concept

Percentage word problems involve finding parts of a whole, comparing quantities, or calculating increases and decreases in real scenarios like salary hikes, discounts, population growth, and election results

💡Key Rules

Always identify the base value first. The base is usually mentioned after 'of' or 'than'. When percentage increases, new value = original + increase. When percentage decreases, new value = original - decrease.

In comparison problems, identify which quantity is 100%

🔑Essential Formulas

- Percentage = (Part/Whole) × 100 - Increase% = (Increase/Original) × 100 - Decrease% = (Decrease/Original) × 100 - New value after x% increase = Original × (100+x)/100 - New value after x% decrease = Original × (100-x)/100 - If A is x% more than B, then B is [x/(100+x)] × 100% less than A

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Exam Patterns

What examiners ask — read before attempting PYQs

SSC CGL typically asks about salary changes, price variations, population problems, election results, and mixture problems. Questions often involve successive percentage changes or finding original values when final values are given. Powerful Shortcut - The 'Of-Is' Method: In any percentage problem, identify the 'OF' value (base/whole) and 'IS' value (part). Then use: Percentage = (IS/OF) × 100. This works for all percentage word problems.

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Worked Example

Solve this step-by-step before moving on

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Step 1

Let original salary = x

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Step 2

After 20% increase = x × 120/100 = 1.2x

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Step 3

After 15% decrease = 1.2x × 85/100 = 1.02x

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Step 4

Given final salary = 10,200

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Step 5

So, 1.02x = 10,200

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Step 6

x = 10,200/1.02 = 10,000 Therefore, original salary = Rs. 10,000 Another Shortcut: For successive percentage changes, if there are a% increase followed by b% decrease, net effect = [a - b - (ab/100)]%. If positive, it's increase; if negative, it's decrease. Using this shortcut: Net effect = 20 - 15 - (20×15/100) = 5 - 3 = 2% increase So final salary = original × 1.02 = 10,200 Original = 10,200/1.02 = 10,000 Common Mistake: Students often confuse the base value. Remember, percentages are always calculated on the original or given base value, not on intermediate results unless specifically mentioned.

🔑 Key Points

Always identify the base value first - it usually comes after 'of' or 'than'
Use 'Of-Is' method: Percentage = (IS value/OF value) × 100
For successive changes: Net effect = a - b - (ab/100) when a% increase then b% decrease
New value after x% increase = Original × (100+x)/100
New value after x% decrease = Original × (100-x)/100
If A is x% more than B, then B is [x/(100+x)] × 100% less than A
In comparison problems, identify which quantity represents 100%
Percentage increase/decrease is always calculated on the original value

📌 Exam Facts

If price increases by 25%, consumption must decrease by 20% to keep expenditure same
When A is 20% more than B, then B is 16.67% less than A
Successive increases of 10% and 20% give net increase of 32%
If population grows by 10% annually, it becomes 1.21 times in 2 years
50% of 40% = 20% (multiply percentages by dividing by 100)
In elections with two candidates, if winner gets 60%, margin of victory is 20%
If salary increases by 15% and tax by 10%, effective increase is 5% on net income

🚀 60-Second Revision

Remember: Base value identification is crucial - look for 'of' and 'than'
Formula: For successive changes a%, b% - Net effect = a + b + (ab/100)
Trick: Use (IS/OF) × 100 for any percentage problem
Trap: Don't calculate percentage on wrong base value
Quick: 25% = 1/4, 20% = 1/5, 50% = 1/2 for faster calculations
Pattern: Original value problems use reverse calculation with given final value

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