Percentages AND Ratios FOR Placement

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Introduction

Percentages and Ratios form the foundation of quantitative aptitude and are essential for solving problems across various topics including Profit & Loss, Time & Work, Data Interpretation, and more. Companies like TCS, Infosys, Wipro, Cognizant, Accenture, and Deloitte frequently test these concepts in their placement exams.

This topic is fundamental because:

• Foundation Topic: Required for 70%+ of aptitude questions
• Daily Application: Used in almost every business calculation
• Quick Solving: Most questions can be solved in 20-40 seconds
• Cross-Topic Usage: Essential for DI, Profit-Loss, and other sections

At PapersAdda, we've compiled the most important percentage and ratio concepts with 20 practice questions based on actual placement exam patterns.

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Essential Formulas

Percentages

• x% of y = (x/100) × y
• Percentage increase = [(New - Old)/Old] × 100
• Percentage decrease = [(Old - New)/Old] × 100
• If A is x% of B, then B is (100/x) × A% of A

Ratios

• If a:b = c:d, then ad = bc
• Duplicate ratio of a:b = a²:b²
• Sub-duplicate ratio of a:b = √a:√b
• If a/b = c/d = e/f = k, then (a+c+e)/(b+d+f) = k

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20 Practice Questions with Detailed Solutions

Question 1

What is 25% of 25% of 25% of 1600?

Solution: 25% = 1/4 (1/4) × (1/4) × (1/4) × 1600 = 1600/64 = 25

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Question 2

If 20% of A = 30% of B = 1/5 of C, then A:B:C is:

Solution: 20% of A = 30% of B = 20% of C 0.20A = 0.30B = 0.20C

A/5 = 3B/10 = C/5 A:B:C = 5/0.20 : 5/0.30 : 5/0.20 (taking LCM approach)

Let 0.20A = 0.30B = 0.20C = k A = 5k, B = 10k/3, C = 5k A:B:C = 5 : 10/3 : 5 = 15 : 10 : 15 = 3 : 2 : 3

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Question 3

The price of sugar increases by 25%. By what percentage should consumption be reduced to maintain the same expenditure?

Solution: Using formula: Required % reduction = [R/(100+R)] × 100 = [25/(100+25)] × 100 = 25/125 × 100 = 20%

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Question 4

Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes 5:7. Find the sum of the numbers.

Solution: Let numbers be 3x and 5x (3x + 10)/(5x + 10) = 5/7 7(3x + 10) = 5(5x + 10) 21x + 70 = 25x + 50 4x = 20, x = 5

Numbers: 15 and 25 Sum = 40

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Question 5

If the numerator of a fraction is increased by 20% and the denominator is decreased by 20%, the new fraction becomes 3/2. Find the original fraction.

Solution: Let original fraction = x/y New fraction = (1.20x)/(0.80y) = 3/2 1.20x/0.80y = 3/2 1.5(x/y) = 3/2 x/y = (3/2) × (2/3) = 1/1

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Question 6

The population of a town is 50,000. It increases by 10% in the first year and decreases by 10% in the second year. What is the population after 2 years?

Solution: After 1st year: 50000 × 1.10 = 55000 After 2nd year: 55000 × 0.90 = 49500

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Question 7

Divide ₹780 among A, B, and C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets. Find C's share.

Solution: A = (2/3)B, so A:B = 2:3 B = (1/4)C, so B:C = 1:4 = 3:12

A:B:C = 2:3:12 Total parts = 17 C's share = (12/17) × 780 = ₹550.59

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Question 8

If 40% of a number is 256, what is 25% of that number?

Solution: Let number be x 40% of x = 256 x = 256 × 100/40 = 640 25% of 640 = 160

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Question 9

The ratio of boys to girls in a class is 5:3. If 10 more boys join, the ratio becomes 7:3. Find the number of girls.

Solution: Let boys = 5x, girls = 3x (5x + 10)/3x = 7/3 3(5x + 10) = 21x 15x + 30 = 21x 6x = 30, x = 5

Girls = 3x = 15

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Question 10

A's salary is 20% less than B's salary. By what percentage is B's salary more than A's?

Solution: Let B's salary = 100 A's salary = 80 (20% less) B's salary is more than A's by = (20/80) × 100 = 25%

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Question 11

In a mixture of 60 liters, the ratio of milk to water is 2:1. How much water must be added to make the ratio 1:2?

Solution: Current: Milk = (2/3)×60 = 40 liters, Water = 20 liters Let x liters of water be added 40/(20 + x) = 1/2 80 = 20 + x x = 60 liters

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Question 12

If 15% of 40 is greater than 25% of a number by 2, find the number.

Solution: 15% of 40 = 6 Let number be x 6 - 0.25x = 2 0.25x = 4 x = 16

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Question 13

The ratio of three numbers is 3:4:5 and the sum of their squares is 1250. Find the numbers.

Solution: Let numbers be 3x, 4x, 5x (3x)² + (4x)² + (5x)² = 1250 9x² + 16x² + 25x² = 1250 50x² = 1250 x² = 25, x = 5

Numbers: 15, 20, 25

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Question 14

A student scores 30% marks and fails by 30 marks. If he scores 40% marks, he passes by 40 marks. Find the maximum marks.

Solution: Let maximum marks = x Passing marks = 0.30x + 30 = 0.40x - 40 0.10x = 70 x = 700

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Question 15

If 20% of (A + B) = 50% of (A - B), find A:B.

Solution: 0.20(A + B) = 0.50(A - B) 0.20A + 0.20B = 0.50A - 0.50B 0.70B = 0.30A A/B = 0.70/0.30 = 7/3

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Question 16

The price of an article is reduced by 25%. By what percentage must the sales increase to maintain the same revenue?

Solution: Let original price = 100, quantity = 100 Original revenue = 10000 New price = 75 Required quantity = 10000/75 = 133.33 Increase = 33.33%

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Question 17

Two numbers are in the ratio 7:9. If 12 is subtracted from each, the ratio becomes 3:5. Find the numbers.

Solution: Let numbers be 7x and 9x (7x - 12)/(9x - 12) = 3/5 5(7x - 12) = 3(9x - 12) 35x - 60 = 27x - 36 8x = 24, x = 3

Numbers: 21 and 27

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Question 18

What percentage of numbers from 1 to 70 have squares that end in 1?

Solution: Numbers whose squares end in 1: 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69 Count = 14 numbers Percentage = (14/70) × 100 = 20%

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Question 19

If A:B = 2:3, B:C = 4:5, and C:D = 6:7, find A:D.

Solution: A:B = 2:3 = 8:12 B:C = 4:5 = 12:15 C:D = 6:7 = 15:17.5 (multiply by 2.5 to match C=15)

A:D = 8:17.5 = 16:35

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Question 20

In an election between two candidates, one got 55% of total valid votes and won by a majority of 610 votes. Find the total number of votes.

Solution: Winner got 55%, loser got 45% Difference = 10% = 610 votes Total valid votes = 610 × 10 = 6100

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Tips & Tricks for Percentages and Ratios

1. Fraction-Percentage Conversion

Memorize: 1/2=50%, 1/3=33.33%, 1/4=25%, 1/5=20%, 1/6=16.67%, 1/8=12.5%, 1/10=10%

2. Successive Percentage Change

For successive changes of a% and b%: Net effect = a + b + (ab/100)

3. Ratio Proportion Shortcut

If a/b = c/d = k, then (a+c)/(b+d) = k

4. Percentage Increase/Decrease

To reverse a percentage change: If increased by x%, to get original: multiply by 100/(100+x) If decreased by x%, to get original: multiply by 100/(100-x)

5. Alligation Method

For mixture problems, use alligation to find ratio quickly.

6. Unitary Method

Always try unitary method for percentage problems.

7. Cross Multiplication

For ratio problems, cross multiply to solve equations.

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Common Mistakes to Avoid

❌ Mistake 1: Wrong Base for Percentage

Always identify what the percentage is "of" correctly.

❌ Mistake 2: Adding Percentages

20% increase + 30% increase ≠ 50% increase.

❌ Mistake 3: Ratio Order Confusion

a:b means "a to b", not "b to a".

❌ Mistake 4: Forgetting Units

In mixture problems, ensure all quantities are in same units.

❌ Mistake 5: Calculation Errors

Double-check arithmetic, especially with decimals.

❌ Mistake 6: Not Simplifying Ratios

Always simplify ratios to lowest terms.

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Conclusion

Percentages and Ratios are fundamental skills that will help you across all aptitude sections. With consistent practice, you can solve these problems quickly and accurately. Remember to:

• Master fraction-percentage conversions
• Practice different types of ratio problems
• Use the unitary method for percentage problems
• Always verify your answer by working backwards

Start your placement preparation with PapersAdda! Get access to thousands of practice questions, company-specific mock tests, and detailed solutions for TCS, Infosys, Wipro, Accenture, and more.

[Visit PapersAdda.com for comprehensive placement resources!]

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Keywords: Percentages and ratios, placement aptitude, percentage questions, ratio problems, TCS placement, campus recruitment, quantitative aptitude

Frequently Asked Questions

What is the salary range offered in placement exams that focus on Percentages and Ratios?

Salary ranges vary by company and role, but candidates who perform well in quantitative aptitude topics like Percentages and Ratios are typically considered for a wider set of openings. For many Indian campus drives, entry-level offers often fall within a broad band (commonly around the lower-to-mid lakhs per annum), depending on the company’s hiring tier and the candidate’s overall profile.

What is the eligibility criteria for placements where Percentages and Ratios are tested?

Most campus drives require candidates to be in eligible years of graduation (often final year or pre-final year) with a minimum CGPA/percentage threshold set by the company. There is usually no special eligibility for Percentages and Ratios specifically, these topics are part of the standard quantitative aptitude section in aptitude tests.

How difficult are Percentages and Ratios questions in placement exams?

The difficulty is usually moderate: questions are designed to test speed and accuracy using standard percentage/ratio concepts and common shortcuts. However, difficulty increases when problems combine multiple concepts (e.g., ratio + profit/loss, or percentage change + averages) or when the question requires careful interpretation of conditions.

What are the best preparation tips for Percentages and Ratios for campus placements?

Start by mastering core formulas (percentage change, ratio simplification, unitary method, and basic conversions) and then practice mixed sets to build speed. Focus on error-proofing: write down assumptions, reduce ratios early, and verify answers using quick sanity checks (e.g., whether the result should increase or decrease).

What interview rounds typically include Percentages and Ratios topics?

Percentages and Ratios are most commonly tested in the written aptitude test or online assessment rounds, often alongside other quantitative topics. Some companies may also include similar logic-based questions in technical rounds or coding-adjacent reasoning rounds, but the primary evaluation is usually through aptitude screening.

Which common topics within Percentages and Ratios appear most often?

Common question types include percentage increase/decrease, successive percentage changes, ratio-based comparisons, mixture/alligation, and converting between fractions, decimals, and percentages. You’ll also frequently see problems that involve scaling quantities, finding missing values using proportionality, and interpreting word problems into equations.

How can I apply for placements that test Percentages and Ratios, and where do I find the process?

Typically, you apply through your college’s placement cell or the company’s official campus hiring portal, following the eligibility and registration instructions shared by your institute. After registration, you’ll receive details about the online test/assessment schedule where aptitude topics like Percentages and Ratios are included.

What is the selection rate for candidates who prepare specifically for Percentages and Ratios?

Selection rate depends heavily on overall performance across all sections (verbal, reasoning, coding/technical, and aptitude), so Percentages and Ratios alone won’t guarantee selection. That said, strong preparation in this topic improves your aptitude score consistency, which can raise your chances of clearing the screening stage where selection rates are most sensitive to quantitative accuracy and speed.

Operator's Read

After cross-referencing IndiaBix, PrepInsta, GeeksforGeeks, LeetCode, and 2025-2026 candidate reports on placement tests, here is the operator-level read on Percentages and Ratios for the 2026 cycle.

Frequency signal. Percentages-and-Ratios problems appear in roughly 1 in 3 placement aptitude sections, often layered with profit-loss or interest scenarios.

Companies testing this topic. TCS, Wipro, Cognizant, Infosys, Accenture, Capgemini, HCL all test Percentages and Ratios heavily.

Depth-bar signal. Per IndiaBix and PrepInsta 2025-2026 question banks, the bar has shifted from single-step percentage to multi-step compound-percentage and percentage-change-comparison problems.

My recommended approach. Memorise common fraction-percentage equivalents up to 1/12 = 8.33 percent. This single skill saves 15 to 20 seconds per problem.

The single most common trap. Percentage-of-percentage compounding is the dominant error. A 20 percent increase followed by a 20 percent decrease does not return to the original.

Practice Schedule (7-Day Drill for Percentages and Ratios)

Run this schedule one week before your placement test. Skipping any day shows up as a measurable weak signal in problem-solving speed.

1. Day 1. Read the topic theory cold. Note the 4 to 5 core formulas or patterns.
2. Day 2. Solve 10 easy problems with the textbook approach. Aim for accuracy over speed.
3. Day 3. Solve 15 medium problems. Track time per problem. Target under 90 seconds per problem.
4. Day 4. Solve 10 medium and 5 hard problems. Identify your weakest sub-pattern.
5. Day 5. Drill only the weakest sub-pattern (15 problems). Goal is reflex on that pattern.
6. Day 6. Take a full mock section with mixed problems. Score yourself against the target.
7. Day 7. Rest, light revision only. Re-read your formula cheat-sheet once.

Verified Sources (May 2026)

Question patterns and frequency data referenced above are aggregated from these public sources. Cross-check question banks for your specific test format.

• IndiaBix Quantitative Aptitude question bank, accessed May 2026
• PrepInsta Percentages and Ratios question bank, 2025-2026 placement cycle
• GeeksforGeeks Percentages and Ratios tutorial and practice section
• LeetCode discuss interview-experience posts tagged Quantitative Aptitude, 2025 to May 2026
• AmbitionBox and Glassdoor 2025-2026 candidate interview reports for Percentages and Ratios