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NDA Basic Percentage

Study Material — 29 PYQs (2018–2023) · Concept Notes · Shortcuts

NDA Basic Percentage is a frequently tested subtopic — 29 previous year questions from 2018–2023 papers are included below with concept notes, key rules and shortcut tricks.

29 PYQs

2018–2023

28 Practice

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10 Key Points

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Previous Year Questions

NDA Basic Percentage — Past Exam Questions

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

Exam Q 12020Previous Year Pattern

A shopkeeper marks an item at ₹500. He offers a discount of 12% on the marked price. What is the selling price of the item?

Exam Q 22023Previous Year Pattern

In an examination, a student scored 72% and obtained 360 marks. What is the total marks of the examination?

Exam Q 32023Previous Year Pattern

A shirt costs ₹800. Its price is increased by 20%. What is the new price?

Exam Q 42023Previous Year Pattern

If 45% of a number is 360, what is 20% of that number?

Exam Q 52023Previous Year Pattern

What is 25% of 480?

Exam Q 62023Previous Year Pattern

A shopkeeper marks an item at ₹500. He offers a discount of 15% on the marked price. What is the selling price?

Exam Q 72023Previous Year Pattern

A book's price was reduced by 30% and now costs ₹490. What was the original price?

Exam Q 82023Previous Year Pattern

In a class of 200 students, 45% are boys. How many girls are there?

Exam Q 92023Previous Year Pattern

If 15% of a number is 45, what is the number?

Exam Q 102023Previous Year Pattern

The price of a commodity increased by 25%. If the new price is ₹750, what was the original price?

Exam Q 112023Previous Year Pattern

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

Exam Q 122023Previous Year Pattern

The price of a commodity increased by 20%, and then decreased by 10%. What is the net percentage change in the price?

Exam Q 132023Previous Year Pattern

A product's price was reduced by 15%, and then the reduced price was increased by 15%. What is the net percentage change from the original price?

Exam Q 142023Previous Year Pattern

The price of petrol increased by 20% and then decreased by 10%. What is the net percentage change?

Exam Q 152023Previous Year Pattern

A shopkeeper marks an item at ₹500. He offers a discount of 12% on the marked price. What is the selling price?

Exam Q 162023Previous Year Pattern

A number is increased by 25%. If the new number is 500, what was the original number?

Exam Q 172018Previous Year Pattern

A student scored marks in three subjects: 75 out of 100 in Maths, 80 out of 100 in English, and 65 out of 100 in Science. What is the overall percentage scored by the student?

Exam Q 182023Previous Year Pattern

In an examination, a student scored 75% marks and obtained 300 marks. What are the total marks for the examination?

Exam Q 192023Previous Year Pattern

A student scored 72% in English and 88% in Mathematics. If English has a weightage of 40% and Mathematics has a weightage of 60%, what is the weighted average percentage?

Exam Q 202020Previous Year Pattern

A shopkeeper marks up the cost price of an item by 40%. He then offers a discount of 10% on the marked price. If the cost price is ₹500, what is his profit percentage?

Exam Q 212023Previous Year Pattern

In an examination, 65% of students passed. If 455 students passed, how many students appeared in total?

Exam Q 222023Previous Year Pattern

A quantity increases by 20%, then decreases by 25%, and finally increases by 10%. What is the net percentage change from the original quantity?

Exam Q 232023Previous Year Pattern

A person's salary is increased by 25% in January and then decreased by 20% in February. If his salary in February is ₹12,000, what was his original salary in December?

Exam Q 242023Previous Year Pattern

A student scored 72% in English, 68% in Mathematics, and 80% in Science. The maximum marks for each subject are 150, 120, and 100 respectively. What is the overall percentage of marks obtained across all three subjects?

Exam Q 252023Previous Year Pattern

In an election, candidate A received 45% of votes, candidate B received 35% of votes, and the remaining votes were invalid. If the total number of valid votes was 8000, how many invalid votes were cast?

Exam Q 262023Previous Year Pattern

A shopkeeper marks up goods by 60% above cost price. He then offers a discount of 25% on the marked price. If the cost price of an item is ₹800, what is his profit percentage?

Exam Q 272023Previous Year Pattern

A container has 120 litres of a mixture containing 40% alcohol. How many litres of pure alcohol must be added to make the alcohol content 60%?

Exam Q 282020Previous Year Pattern

A shopkeeper marks up goods by 60% above cost price. He then offers a discount of 25% on the marked price during a sale. Later, he realizes his profit margin is lower than expected and increases the selling price by 20%. What is his final profit percentage?

Exam Q 292023Previous Year Pattern

The price of a commodity increases by 20% in the first year and decreases by 15% in the second year. If the final price is ₹1224, what was the original price?

Concept Notes

Basic Percentage— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic

BASIC PERCENTAGE — COMPLETE EXAM GUIDE --- CORE CONCEPT ---

Percentage means 'per hundred'. It is a way to express a number as a part of 100. The word comes from Latin 'per centum' meaning 'out of 100'. Simple idea: If you score 45 out of 50, what is your percentage? You convert that fraction into 'out of 100'. That number is your percentage.

Think of percentage as a universal comparison tool. It lets you compare any two quantities on the same scale of 100. ---

2.Key Rules

Core rules you must know cold

Rule 2

The base changes depending on the question. Always identify WHAT you are taking the percentage OF

Rule 3

Percentage has no unit. It is a pure number

Rule 4

A percentage can be greater than 100

Example

150% of 200 = 300. ---

3.Formula Block

Memorise — at least one formula appears in every paper

Percentage = (Part / Whole) x 100

Part = (Percentage / 100) x Whole

Whole = (Part x 100) / Percentage

Example: 3/4 = (3/4) x 100 = 75%

Example: 40% = 40/100 = 2/5

Basic Formula:

To find Part when Percentage is given:

To find Whole when Part and Percentage are given:

Fraction to Percentage:

Multiply fraction by 100

Percentage to Fraction:

Divide by 100

---

4.Exam Patterns

What examiners ask — read before attempting PYQs

--- SSC CGL and other exams ask percentage questions in these forms: 1. Direct calculation — 'What is 35% of 480?' 2. Finding the base — '25% of what number is 75?' 3. Percentage increase or decrease — 'A number increases from 80 to 100.

What is the % increase?' 4. Expressing one quantity as a percentage of another — 'What % is 45 of 180?' 5. Finding a number when its percentage value is known. Formula for % Change: % Change = [(New Value - Old Value) / Old Value] x 100 If result is positive = % Increase. If negative = % Decrease. ---

5.Shortcuts

Use these to save 30–60 seconds per question

Trick 2 — Percentage of Percentage Shortcut

X% of Y = Y% of X Example: 16% of 25 = 25% of 16 = 4. Much easier! Trick 3 — Quick % Calculation: To find any % quickly, break it into easy parts

Example

17.5% of 400 = 10% of 400 + 5% of 400 + 2.5% of 400 = 40 + 20 + 10 = 70 This avoids long multiplication. ---

6.Worked Example

Solve this step-by-step before moving on

1

Step 1

Recognise that 37.5% = 3/8 (memorised fraction)

2

Step 2

Apply: (3/8) x 960

3

Step 3

960 / 8 = 120

4

Step 4

120 x 3 = 360 Answer: 360 Time taken using trick: 8 seconds. Using multiplication: 40+ seconds. --- WORKED EXAMPLE 2 --- Question: A number is increased from 240 to 300. What is the percentage increase?

1

Step 1

Find the increase = 300 - 240 = 60

2

Step 2

Apply formula: % Increase = (60 / 240) x 100

3

Step 3

Simplify: 60/240 = 1/4

4

Step 4

1/4 x 100 = 25% Answer: 25% increase Key Note: The BASE is always the ORIGINAL (OLD) value, not the new value. ---

7.Exam Traps

Common mistakes students make — avoid these

(THE NUMBER 1 TRAP) --- Trap: Students use the WRONG BASE when calculating % increase or decrease. Wrong thinking: 'The number changed from 80 to 100, so increase is 20, base is 100.' Right thinking: 'Base is always the ORIGINAL number, which is 80.' Wrong answer: (20/100) x 100 = 20% Correct answer: (20/80) x 100 = 25% This single mistake causes 2-3 wrong answers per paper. Never forget: ORIGINAL = BASE.

Key Points to Remember

Percentage means 'per hundred' — always a comparison out of 100.
Formula: Percentage = (Part / Whole) x 100.
To find the Part: Part = (Percentage / 100) x Whole.
To find the Whole (base): Whole = (Part x 100) / Percentage.
Shortcut: X% of Y = Y% of X. Use whichever is easier to calculate.
% Change Formula: [(New Value - Old Value) / Old Value] x 100.
Base in % increase/decrease is ALWAYS the original (old) value, never the new value.
Key fractions: 1/4 = 25%, 1/8 = 12.5%, 3/8 = 37.5%, 1/3 = 33.33%, 2/3 = 66.67%.
Percentage can exceed 100 — there is no upper limit to a percentage value.
Shortcut for quick calculation: Break any % into 10%, 5%, 1% parts and add.

Exam-Specific Tips

37.5% = 3/8 as a fraction — this conversion appears frequently in SSC CGL data interpretation and arithmetic questions.
16.67% = 1/6 exactly — knowing this avoids decimal confusion in exam calculations.
% Change formula: [(New - Old) / Old] x 100 — the denominator is always the OLD value, not the new value.
X% of Y equals Y% of X — this property is tested directly as a conceptual MCQ in banking and SSC exams.
1/7 = 14.2857...% (approximately 14.28%) — a commonly tested repeating decimal percentage.
If a value increases by 100%, it becomes double the original value (200% of original).
12.5% = 1/8 — one of the most frequently appearing percentage-fraction conversions in SSC CGL Tier 1.

Practice MCQs

Basic Percentage — Practice Questions

28graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 28

All MCQs →

Practice 1easy

A book's price is reduced from ₹500 to ₹400. What is the percentage decrease?

Practice 2easy

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

Practice 3easy

A shopkeeper marks an item at ₹500. He offers a 20% discount. What is the selling price?

Practice 4easy

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

Practice 5easy

In an exam, 65% of students passed. If 260 students passed, how many students took the exam?

Practice 6easy

A shirt costs ₹800. Its price is increased by 20%. What is the new price?

Practice 7easy

If 15% of a number is 45, what is the number?

Practice 8easy

What is 25% of 480?

Practice 9easy

A shopkeeper marks the price of an item at ₹500. He offers a discount of 12% on the marked price. What is the selling price of the item?

Practice 10easy

In a class of 80 students, 35% are girls. How many boys are there in the class?

Practice 11easy

If 45% of a number is 360, what is 25% of that number?

Practice 12medium

A shopkeeper marks an item at ₹500. He offers a discount of 12% on the marked price. What is the selling price?

Practice 13medium

A number is increased by 30%, and then the result is decreased by 30%. Is the final number greater than, less than, or equal to the original number?

Practice 14medium

A number is increased by 25%, and then the result is decreased by 20%. What is the net percentage change from the original number?

Practice 15medium

A shopkeeper marks up the cost price of an item by 40%. He then offers a discount of 10% on the marked price. If the cost price is ₹500, what is his profit percentage?

Practice 16medium

In an examination, a student scored 72% marks and obtained 360 marks. What are the total marks of the examination?

Practice 17medium

The price of a commodity increases by 25% and then decreases by 20%. What is the net percentage change in the price?

Practice 18medium

A student's marks increased from 45 to 54. What is the percentage increase in marks?

Practice 19medium

A shopkeeper buys goods for ₹800 and sells them at a profit of 35%. What is the selling price?

Practice 20medium

In an examination, 65% of students passed. If 455 students passed, how many students appeared in total?

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60-Second Revision — Basic Percentage

Formula: Percentage = (Part / Whole) x 100. Rearrange to find Part or Whole as needed.
Trap: In % increase or decrease, ALWAYS divide by the ORIGINAL (old) value, never the new value.
Shortcut: Use X% of Y = Y% of X to pick the easier calculation and save time.
Memorise: 1/8=12.5%, 3/8=37.5%, 1/6=16.67%, 1/3=33.33%, 2/3=66.67% for instant conversion.
Quick calc trick: Break any % into 10%+5%+1% chunks and add — avoids long multiplication.
Remember: Percentage has no unit and CAN be more than 100% — do not assume a cap of 100.
% Change = [(New - Old) / Old] x 100. Positive answer = increase. Negative answer = decrease.

Percentage Change→

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