Percentages AND Ratios FOR Placement

Meta Description: Master Percentages and Ratios for campus placements with 20 solved questions, shortcut formulas, and expert tips. Essential for TCS, Infosys, Wipro, and all major companies.

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.

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

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

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

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%

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

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

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

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

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

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

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%

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

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

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

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

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

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%

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

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%

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

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

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.

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.

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

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