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SSC CPO Percentage Word Problems

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This page covers SSC CPO Percentage Word Problems with complete concept notes, 13 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

13graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A student scored 72% in an exam and obtained 360 marks. What are the total marks of the exam?

Practice 2easy

A company's profit increased from ₹50,000 to ₹65,000. What is the percentage increase in profit?

Practice 3easy

A shopkeeper sells an item at ₹480, which is 20% more than its cost price. What is the cost price of the item?

Practice 4easy

In an exam, 65% of students passed. If 455 students passed, how many students appeared for the exam?

Practice 5medium

In an examination, 35% of students failed in Hindi, 28% failed in English, and 20% failed in both subjects. What percentage of students passed in both subjects?

Practice 6medium

A shopkeeper marks his goods at 40% above the cost price. He then offers a discount of 20% on the marked price. What is his profit percentage?

Practice 7medium

A student scored 65% marks in one exam and 75% marks in another exam. If the first exam had 80 questions and the second had 120 questions, what is the overall percentage of marks obtained?

Practice 8medium

The price of petrol increased by 25% last month. This month, it decreased by 20%. If the current price is ₹84 per litre, what was the price two months ago?

Practice 9medium

A company's revenue increased from ₹50 lakhs to ₹65 lakhs. In the same period, expenses increased from ₹30 lakhs to ₹39 lakhs. By what percentage did the profit increase?

Practice 10hard

In an election, Candidate A received 45% of votes, Candidate B received 35% of votes, and Candidate C received the remaining votes. If A won by 2,000 votes over B, how many votes did C receive?

Practice 11hard

A shopkeeper marks up goods by 60% above cost price. He then offers a discount of 25% on the marked price during a sale. If the cost price of an item is ₹400, what is his profit percentage?

Practice 12hard

In a college, 40% of students are in Science, 35% are in Commerce, and the remaining are in Arts. If 20% of Science students and 30% of Commerce students pass an entrance exam, what percentage of the total student population passes the exam?

Practice 13hard

A container has 200 litres of milk. Each day, 25% of the milk is removed and replaced with water. After 2 days, what is the percentage of milk in the container?

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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