Percentage, Ratio and Average Test: IQ and Logical Reasoning Questions, Tricks, and Practice

Percentage, Ratio, and Average Test is an important part of IQ and Logical Reasoning that tests your ability to calculate percentages, compare quantities using ratios, and determine averages in different situations.

For Officer Cadet Entrance Exam preparation, these questions help develop numerical ability, arithmetic skills, comparative reasoning, and problem-solving accuracy. Explore the complete Officer Cadet Exam resources and IQ for Officer Cadet preparation for additional practice and study materials.

What is Percentage, Ratio, and Average Test?

Percentage, Ratio, and Average are three interconnected concepts used to compare quantities, express proportions, and find central values in a data set.
👉 Percentage – a number expressed as a fraction of 100, denoted by “%,” where “percent” literally means “per hundred”
👉 Ratio – a comparison of two or more quantities of the same kind, expressed as a : b
👉 Average (arithmetic mean) – the sum of all observations divided by the number of observations, representing the central value of a data set
Example:
What is 25% of 200?
Taking 25 parts out of every 100 from a total of 200 gives the part directly.
Answer: 50
These concepts show up constantly in real life — calculating discounts and profit margins, comparing population or demographic data, working out average scores or expenditures, and analyzing data in economics and statistics.

What Skills Do These Questions Measure?

Percentage, ratio, and average questions test your ability in:
👉 Arithmetic calculation – working accurately with fractions, decimals, and whole numbers
👉 Understanding of proportional relationships – seeing how parts relate to wholes and to each other
👉 Comparing quantities – using ratios to express relative size
👉 Applying formulas quickly – matching the right formula to what’s given
👉 Speed and accuracy – solving multi-step problems under exam time pressure

These topics score high in Numerical Reasoning because they follow predictable formulas:
👉 Percentages: finding a percentage of a number, one number as a percentage of another, successive changes, and population/depreciation problems
👉 Ratios: dividing quantities in a given ratio, comparing ratios, and solving proportions
👉 Averages: basic averages, missing number from an average, weighted averages, and age-based problems

Important Terms and Definitions

👉 Percentage – a number expressed as a fraction of 100: Percentage = (Part / Whole) × 100
👉 Fraction to percentage – multiply the fraction by 100; for example, 3/4 × 100 = 75%
👉 Percentage to fraction – divide by 100 and simplify; for example, 25% = 25/100 = 1/4
👉 Ratio – a comparison of two quantities of the same kind, written a : b, where 2 : 3 means for every 2 units of the first quantity there are 3 units of the second
👉 Proportion – an equation stating two ratios are equal; if a : b = c : d, then a, b, c, and d are in proportion (for example, 2 : 3 = 4 : 6)
👉 Average (arithmetic mean) – Average = Sum of all observations / Number of observations
👉 Weighted average – used when observations carry different weights: Weighted Average = (w₁x₁ + w₂x₂ + …) / (w₁ + w₂ + …)

Fundamental Formulas

Percentage Formulas

Successive Percentage Change Formula

For two successive percentage changes of x% and y%:
Net % Change = x + y + (xy / 100)
This works for two successive increases, two successive decreases (using negative values), or one increase and one decrease (using the appropriate signs).

Ratio Formulas

Average Formulas

Types of Percentage, Ratio, and Average Questions

These problems generally fall into a handful of recurring patterns:

1. Basic Percentage Calculation

Finding a Percentage of a Given Number
Example:
Find 35% of 800.
Solution:
35% of 800 = (35 ÷ 100) × 800
= 0.35 × 800
= 280
Answer: 280

2. Finding Percentage of One Number to Another

Expressing one value as a percentage of another
Example:
40 is what percent of 160?
Solution:
Percentage = (Part ÷ Whole) × 100
Percentage = (40 ÷ 160) × 100
Percentage = 0.25 × 100
Percentage = 25%
Answer: 25%

3. Successive Percentage Change

Combining two or more percentage changes into a single net effect.
Example:
A number is increased by 10% and then decreased by 10%. What is the net percentage change?
Solution:
Using the successive change formula:
Net % Change = x + y + (xy ÷ 100)
Here, x = +10 and y = −10
Net % Change = 10 + (−10) + (10 × −10) ÷ 100
Net % Change = 0 + (−100 ÷ 100)
Net % Change = 0 − 1
Net % Change = −1%
A negative value means a net decrease.
Answer: 1% decrease

4. Basic Ratio Problems

Splitting a quantity according to a given ratio
Example:
Divide 360 in the ratio 2 : 3 : 4.
Solution:
Sum of ratio terms = 2 + 3 + 4 = 9
First part = (2 ÷ 9) × 360 = 80
Second part = (3 ÷ 9) × 360 = 120
Third part = (4 ÷ 9) × 360 = 160
Answer: 80, 120, 160

5. Finding a Missing Number in a Ratio

Solving a proportion to find an unknown value
Example:
If 3 : 5 = x : 20, find x.
Solution:
3 : 5 = x : 20
Using cross-multiplication:
3 × 20 = 5 × x
60 = 5x
x = 60 ÷ 5
x = 12
Answer: 12

6. Basic Average Calculation

Finding the mean of a set of values
Example:
Find the average of 10, 20, 30, 40, 50.
Solution:
Sum of all observations = 10 + 20 + 30 + 40 + 50 = 150
Number of observations = 5
Average = Sum of all observations ÷ Number of observations
Average = 150 ÷ 5 = 30
Answer: 30

7. Finding a Missing Number from a Given Average

Working backward from a known mean to find a missing number
Example:
The average of 5 numbers is 20. If four numbers are 15, 18, 22, 25, find the fifth number.
Solution:
Total sum of all 5 numbers = 20 × 5 = 100
Sum of the four known numbers = 15 + 18 + 22 + 25 = 80
Fifth number = Total sum − Sum of known numbers
Fifth number = 100 − 80 = 20
Answer: 20

8. Weighted Average

Combining groups of different sizes and averages into one overall average
Example:
A class has 20 boys with average weight 50 kg and 30 girls with average weight 45 kg. Find the average weight of the whole class.
Solution:
Total weight of boys = 20 × 50 = 1000 kg
Total weight of girls = 30 × 45 = 1350 kg
Combined weight of whole class = 1000 + 1350 = 2350 kg
Total number of students = 20 + 30 = 50
Average weight of whole class = 2350 ÷ 50 = 47 kg
Answer: 47 kg

9. Combined Percentage and Ratio Problems

Applying both concepts together within a single problem
Example:
A bag contains coins in the ratio 2 : 3 : 4 of denominations Rs 10, Rs 5, and Rs 2 respectively. If the total value is Rs 430, find the number of Rs 10 coins.
Solution:
Let the number of coins be 2x, 3x, and 4x respectively.
Value of Rs 10 coins = 2x × 10 = 20x
Value of Rs 5 coins = 3x × 5 = 15x
Value of Rs 2 coins = 4x × 2 = 8x
Total value = 20x + 15x + 8x = 43x
Given, total value = Rs 430
So, 43x = 430
x = 430 ÷ 43
x = 10
Number of Rs 10 coins = 2x = 2 × 10 = 20
Answer: 20 coins

10. Age-Based Average Problems

A variation involving people joining or leaving a group over time
Example:
The average age of 20 students is 15 years. If the teacher’s age is included, the average becomes 16 years. Find the teacher’s age.
Solution:
Total age of 20 students = 20 × 15 = 300 years
Total age of 21 people (students + teacher) = 21 × 16 = 336 years
Teacher’s age = Total age of 21 people − Total age of 20 students
Teacher’s age = 336 − 300 = 36 years
Answer: 36 years

How to Solve These Questions

Follow this step-by-step method during your exam.

Step 1: Read the Question Carefully

Identify what’s given — the part and whole for percentage problems, the quantities being compared for ratio problems, or the observations for average problems.

Step 2: Identify the Type of Question

Determine whether it’s a percentage calculation, a ratio comparison, an average calculation, or a combination of concepts.

Step 3: Select the Correct Formula

Choose the formula that matches what’s given and what you’re solving for.

Step 4: Set Up the Equation

Write out the equation using the formula you selected.

Step 5: Solve Step by Step

Work through the calculation carefully, especially when fractions or decimals are involved.

Step 6: Verify Your Answer

Check that the result is logical: a percentage should fall between 0% and 100% unless it represents an increase or decrease, a ratio should be in its simplest form, and an average should fall between the minimum and maximum values in the data set.

Effective Tricks to Solve These Questions

Trick 1: Use Percentage Equivalents
👉 Memorize common percentage-fraction equivalents for faster calculation: 10% = 1/10, 12.5% = 1/8, 20% = 1/5, 25% = 1/4, 33⅓% = 1/3, 50% = 1/2, 66⅔% = 2/3, 75% = 3/4.
Trick 2: Use Multiplication Factors
👉 Instead of calculating percentages step by step, multiply the number directly — 25% is the same as multiplying by 0.25 (or dividing by 4), 20% as multiplying by 0.20 (or dividing by 5), and 50% as multiplying by 0.50 (or dividing by 2).
Trick 3: Always Simplify Ratios
👉 Reduce every ratio to its simplest form by dividing both terms by their highest common factor.
Trick 4: Use Cross-Multiplication for Proportions
👉 For a : b = c : d, use ad = bc to solve for a missing value quickly.
Trick 5: Use the Shortcut for a Changing Average
👉 When a new value is added and the average increases, the relationship between the old average, the increase, and the new value can be worked out directly without recalculating the whole sum from scratch.
Trick 6: Use the Unitary Method for Ratios
👉 Find the value of a single unit first, then multiply it out to get each part of the ratio.
Trick 7: Apply the Successive Percentage Formula
👉 Use x + y + (xy/100) whenever you’re combining two percentage changes into one net figure.
Trick 8: Use Assumed Values for Complex Problems
👉 For problems without concrete numbers, assume a convenient value like 100 or 100x to simplify the algebra.

Important Tips to Solve These Questions

Common Mistakes to Avoid
👉 Taking a percentage of the wrong base — always confirm whether the percentage applies to the original value or a changed one.
👉 Adding percentage changes directly — two successive percentage changes rarely add up simply; use the net % change formula instead.
👉 Leaving ratios unsimplified — an unreduced ratio can look like a wrong answer even when the underlying value is correct.
👉 Confusing simple and weighted averages — a weighted average is not the same as averaging the group averages directly; the group sizes matter.
👉 Forgetting to update the count in average problems — when someone joins or leaves a group, both the sum and the number of observations change.

Quick Solving Checklist
Before selecting your answer, use this checklist:
👉 Read the question carefully.
👉 Identified the type of problem (percentage, ratio, average, or mixed).
👉 Selected the correct formula.
👉 Converted percentages to fractions where helpful.
👉 Simplified ratios to their lowest terms.
👉 Performed the calculations carefully.
👉 Verified the answer makes logical sense.
👉 Avoided spending too much time on one question.

Practice Questions

Conclusion

Mastering the Percentage, Ratio, and Average Test is essential for the Nepal Army Officer Cadet Entrance Examination. Success requires systematic application of formulas and concepts — not guesswork — across scenarios involving proportional relationships, comparative analysis, and central tendency calculations.

Follow this disciplined approach:
Read → Identify → Apply Formula → Calculate → Verify → Answer
Regular practice enhances pattern recognition, speed, logic, and accuracy. Percentage, Ratio, and Average form the foundation of many numerical reasoning problems, and with the right formulas, conversion shortcuts, and the unitary method, these questions can be solved quickly and accurately.

This resource is part of the Officer Cadet Entrance Exam Preparation series, focusing on IQ and Logical Reasoning for the Nepal Army Officer Cadet Entrance Exam. For structured lessons, comprehensive practice banks, and mock tests, explore the Percentage, Ratio, and Average Test subtopic under the Verbal Reasoning Test topic in the IQ and Logical Reasoning course on the Pratima Academy LMS.

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