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NDA Percentage Change

Study Material — 15 PYQs (2018–2023) · Concept Notes · Shortcuts

NDA Percentage Change is a frequently tested subtopic — 15 previous year questions from 2018–2023 papers are included below with concept notes, key rules and shortcut tricks.

15 PYQs
2018–2023
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Previous Year Questions

NDA Percentage Change — Past Exam Questions

15 questions from actual NDA papers · all shown free · click option to reveal solution

Exam Q 12020Previous Year Pattern

The price of a commodity increases by 25% in the first year. In the second year, the price decreases by 20% from the increased price. What is the net percentage change in the price over the two years?

Exam Q 22023Previous Year Pattern

A student scored 72 marks out of 120 in an exam. What is the percentage of marks obtained?

Exam Q 32023Previous Year Pattern

A shopkeeper reduced the price of a shirt from ₹800 to ₹600. What is the percentage decrease?

Exam Q 42018Previous Year Pattern

The price of a shirt increased from ₹400 to ₹500. What is the percentage increase in the price?

Exam Q 52023Previous Year Pattern

The number of employees in a company increased from 400 to 500. What is the percentage increase in the number of employees?

Exam Q 62023Previous Year Pattern

The price of a book increased from ₹200 to ₹250. What is the percentage increase in price?

Exam Q 72023Previous Year Pattern

The population of a town increased from 50,000 to 60,000. What is the percentage increase in population?

Exam Q 82023Previous Year Pattern

A student's marks increased from 60 to 75. What is the percentage increase in marks?

Exam Q 92023Previous Year Pattern

A mobile phone's price decreased from ₹15,000 to ₹12,000. What is the percentage decrease in price?

Exam Q 102023Previous Year Pattern

The population of a town was 50,000 in 2020. If it increased by 20% in 2021, what was the population in 2021?

Exam Q 112023Previous Year Pattern

The price of a commodity increases by 25% in the first year and then decreases by 20% in the second year. What is the net percentage change in price over the two years?

Exam Q 122020Previous Year Pattern

The price of a commodity increases by 25% in the first year. In the second year, the new price decreases by 20%. If the final price is ₹600, what was the original price?

Exam Q 132023Previous Year Pattern

A shopkeeper buys goods at ₹800 per unit. He marks up the price by 40% and then offers a discount of 15% on the marked price. What is the profit percentage?

Exam Q 142018Previous Year Pattern

The price of a laptop was increased by 20% and then decreased by 15%. What is the net percentage change in the price of the laptop?

Exam Q 152020Previous Year Pattern

The price of a commodity increases by 25% in the first year. In the second year, it decreases by 20% of the new price. In the third year, it increases by 10% of the price at the end of the second year. If the final price is ₹1,980, what was the original price?

Concept Notes

Percentage Change— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic
Think of it this way

A shirt costs Rs. 200 today and Rs. 250 tomorrow. How much did the price rise in percentage terms? That answer is a Percentage Change

There are only two types

• Percentage Increase — new value is MORE than original • Percentage Decrease — new value is LESS than original ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

2.Formula Block

Memorise — at least one formula appears in every paper
Percentage Change = [(New Value - Original Value) / Original Value] x 100
If the result is POSITIVE → Percentage Increase
If the result is NEGATIVE → Percentage Decrease (ignore the minus sign and say 'decreased by')
% Change = (Change / Original) x 100

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Short form:

Always divide by the ORIGINAL (old) value — not the new value.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

3.Key Rules

Core rules you must know cold
Rule 2

Percentage change can be more than 100% (if something more than doubles)

Rule 3

Percentage change is never less than -100% (a thing cannot decrease by more than its full value)

Rule 4

If a value increases by x% and then decreases by x%, the final value is NOT the same as original. It is always LESS. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

4.Exam Patterns

What examiners ask — read before attempting PYQs

— WHAT GETS ASKED ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ SSC CGL tests Percentage Change in these ways: 1. Direct calculation — find % increase or decrease between two numbers 2. Salary/Price problems — price goes up by 20%, find new price or original price 3. Successive change — price changes twice, find net effect 4.

Population problems — population grows by x% per year 5. Reverse percentage — new value given, find original value ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

5.Shortcuts

Use these to save 30–60 seconds per question
TRICK 2 — Multiplying Factor Method

Instead of calculating step by step, use multiplying factors. 20% increase → multiply by 1.20 15% decrease → multiply by 0.85 30% increase → multiply by 1.30 For successive changes, just multiply the factors together

Example

20% increase then 10% decrease = 1.20 x 0.90 = 1.08 → 8% net increase TRICK 3 — Reverse Percentage (Finding Original Value): If after a 20% increase the new value is 480: Original = 480 / 1.20 = 400 Formula: Original = New Value / (1 + r/100) for increase Original = New Value / (1 - r/100) for decrease ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

6.Worked Example

Solve this step-by-step before moving on
1
Step 1

Find the change. Change = 96 - 80 = 16

2
Step 2

Divide by the ORIGINAL value. 16 / 80 = 0.20

3
Step 3

Multiply by 100. 0.20 x 100 = 20% Answer: Petrol price increased by 20%. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ WORKED EXAMPLE 2 — SUCCESSIVE CHANGE ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Question: A shopkeeper increases the price of an item by 30% and then decreases it by 10%. What is the net percentage change? Method 1 — Formula: Net % Change = a + b + (a x b)/100 = 30 + (-10) + (30 x -10)/100 = 30 - 10 - 3 = 17% Answer: Net increase of 17%. Method 2 — Multiplying Factor (verify): 1.30 x 0.90 = 1.17 → 17% increase. Same answer. Correct! ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ NUMBER ONE

7.Exam Traps

Common mistakes students make — avoid these

— EXAM TRAP ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ STUDENTS USE THE NEW VALUE AS THE BASE INSTEAD OF THE ORIGINAL VALUE. Example trap: Price goes from Rs. 100 to Rs. 125. Some students calculate: (25/125) x 100 = 20%. WRONG! Correct: (25/100) x 100 = 25%. Always ask yourself: 'What was the value BEFORE the change?' That is your base.

Always divide by THAT number.

Key Points to Remember

  • Percentage Change = (Change / Original Value) x 100 — always divide by the ORIGINAL.
  • Positive result means Percentage Increase; negative result means Percentage Decrease.
  • SHORTCUT: Successive % change formula = a + b + (ab/100), where a and b are the two changes.
  • SHORTCUT: Multiplying Factor for increase of r% is (1 + r/100); for decrease of r% is (1 - r/100).
  • SHORTCUT: To find original value after r% increase, divide new value by (1 + r/100).
  • If a value increases by x% then decreases by x%, net result is always a DECREASE of (x squared)/100 %.
  • Percentage change CAN exceed 100% if the value more than doubles.
  • Percentage change CANNOT be less than -100% since a value cannot fall below zero.
  • In successive changes, multiply the multiplying factors together to get the net effect directly.
  • The most common exam trap is dividing by the NEW value instead of the ORIGINAL value — never do this.

Exam-Specific Tips

  • Formula: Net % change after two successive changes a% and b% = a + b + (ab/100).
  • If price increases by 20% then decreases by 20%, net change = -4% (a loss of 4%, not zero).
  • Multiplying factor for a 25% increase = 1.25; for a 25% decrease = 0.75.
  • To reverse a 20% increase: divide the new value by 1.20 to get the original value.
  • If a value doubles, the percentage increase is exactly 100%.
  • If a value becomes zero, the percentage decrease is exactly 100%.
  • Two successive increases of 10% each give a net increase of 21%, not 20% (using formula: 10+10+1=21).
Practice MCQs

Percentage Change — Practice Questions

34graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 34

All MCQs →
Practice 1easy

If the population of a town was 50,000 and it increased by 20%, what is the new population?

Practice 2easy

The price of a commodity increases by 25% in the first month and then decreases by 20% in the second month. What is the net percentage change in the price over the two months?

Practice 3easy

The price of a book increased from ₹200 to ₹250. What is the percentage increase in price?

Practice 4easy

A student's marks increased from 60 to 75. What is the percentage increase in marks?

Practice 5easy

A student scored 72 marks out of 120 in an exam. What is the percentage of marks obtained?

Practice 6easy

The salary of an employee was ₹30,000 per month. It was increased by 15%. What is the new salary?

Practice 7easy

The price of petrol decreased from ₹100 per litre to ₹80 per litre. What is the percentage decrease?

Practice 8easy

The population of a village decreased from 5000 to 4500. What is the percentage decrease in population?

Practice 9easy

A shopkeeper reduced the price of a shirt from ₹800 to ₹600. What is the percentage decrease in price?

Practice 10easy

A shopkeeper reduced the price of a shirt from ₹800 to ₹600. What is the percentage decrease?

Practice 11medium

The population of a town increases by 10% in the first year. In the second year, it decreases by 5%. In the third year, it increases by 8%. What is the net percentage change in population after three years?

Practice 12medium

A shopkeeper marks up goods by 60% above cost price. He then offers a discount of 25% on the marked price. What is his profit percentage?

Practice 13medium

The price of a commodity increases by 25% in the first year. In the second year, it decreases by 20% of the new price. If the original price was ₹800, what is the percentage change in price over the two years?

Practice 14medium

A number is increased by 50% and then decreased by 50%. What is the net percentage change?

Practice 15medium

A student's marks increased from 45 to 54. Later, the marks were recalculated and decreased from 54 to 48. What is the net percentage change in marks from the original value of 45?

Practice 16medium

A shopkeeper buys goods at ₹500 per unit. He marks up the price by 40% but then offers a discount of 10% on the marked price. What is his profit percentage?

Practice 17medium

The value of a car depreciates by 20% in the first year and 15% in the second year. If the initial value was ₹5,00,000, what is the value after two years?

Practice 18medium

The price of a commodity increases by 25% in the first year and then decreases by 20% in the second year. What is the net percentage change in price over the two years?

Practice 19medium

The value of a car depreciates by 15% in the first year and 10% in the second year. If the initial value was ₹5,00,000, what is the value after two years?

Practice 20medium

A shopkeeper marks up goods by 40% above cost price. He then offers a discount of 25% on the marked price. What is his profit percentage?

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60-Second Revision — Percentage Change

  • Formula: % Change = (New - Old) / Old x 100. Base is ALWAYS the OLD (original) value.
  • Trap: Never divide by the new value. Dividing by new value is the single most common mistake in this topic.
  • Successive change shortcut: Net % = a + b + ab/100. Use this for any two back-to-back % changes.
  • Multiplying factor method: increase by r% → multiply by (1 + r/100); decrease by r% → multiply by (1 - r/100). Chain them for successive changes.
  • Reverse % trick: Original = New Value divided by (1 + r/100) for increase OR (1 - r/100) for decrease.
  • Remember: +x% then -x% always gives a NET LOSS of (x squared)/100 %. Example: +10% then -10% = -1% net.
  • Quick check method: Use multiplying factors and verify with the successive formula — both must give the same answer.
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