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Agniveer Army CEE Percentage Word Problems

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This page covers Agniveer Army CEE Percentage Word Problems with complete concept notes, 8 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Percentage Word Problems— Rules & Concept

Core ConceptRead 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%.

Formula BlockMemorise — at least one formula appears in every paper
- 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
Exam PatternsWhat 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.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Let original salary = x

2
Step 2

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

3
Step 3

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

4
Step 4

Given final salary = 10,200

5
Step 5

So, 1.02x = 10,200

6
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

Exam TrapsCommon mistakes students make — avoid these

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 to Remember

  • 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-Specific Tips

  • 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
Practice MCQs

Percentage Word Problems — Practice Questions

8graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A shopkeeper bought a shirt for ₹400 and sold it at a profit of 25%. What is the selling price?

Practice 2easy

In a school, 60% of students are boys. If there are 150 boys, how many total students are in the school?

Practice 3easy

The price of a book was reduced by 20% during a sale. If the original price was ₹500, what is the sale price?

Practice 4medium

A shopkeeper bought a shirt for ₹400. He marked it at 50% above the cost price and then gave a 20% discount on the marked price. What is the selling price?

Practice 5medium

In a school, 60% of students passed in Mathematics and 75% passed in Science. If 45% passed in both subjects, what percentage of students failed in both subjects?

Practice 6medium

A candidate scored 72% marks in an exam and obtained 360 marks. What were the total marks for the exam?

Practice 7medium

The price of petrol increased by 25% last month and then decreased by 20% this month. If the original price was ₹80 per litre, what is the current price?

Practice 8hard

A shopkeeper buys a shirt for ₹400. He marks up the price by 50% and then offers a discount of 20% on the marked price. What is his profit percentage?

60-Second Revision — Percentage Word Problems

  • 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
←Population Problems
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