Ratio Questions Explained: How to Solve Them in Aptitude Tests

Ratio questions are among the most frequently tested topics in numerical reasoning assessments. Whether you are applying for a graduate scheme at Deloitte, a technology role at Google, a finance position at JP Morgan, or a fast-track programme in the Civil Service, you will almost certainly encounter ratio problems as part of the recruitment process. Employers use these questions because they reveal how well you handle quantitative comparisons, proportional thinking, and multi-step calculations under time pressure.

Despite their importance, many candidates find ratio questions intimidating. The good news is that the underlying mathematics is straightforward. Once you understand the core principles and practise applying them to different question formats, you can solve ratio problems quickly and accurately. This guide breaks down every type of ratio question you are likely to face in an aptitude test, walks you through worked examples, and gives you strategies for handling even the most complex multi-step problems.

What Is a Ratio and Why Does It Matter in Aptitude Tests?

A ratio is a way of comparing two or more quantities by showing their relative sizes. When we write 3:2, we mean that for every 3 units of the first quantity, there are 2 units of the second. Ratios do not tell you the actual amounts involved. They only tell you the relationship between the amounts.

This distinction is important because aptitude test questions often require you to move between the ratio and the actual values. You might be given a ratio and a total, and asked to find individual amounts. Or you might be given actual figures and asked to express them as a ratio. Both directions require a clear understanding of what a ratio represents.

Ratios can be written in several ways. The ratio of A to B can be expressed as A:B, as A/B, or in words as "A to B." In aptitude tests, the colon notation is most common, but you should be comfortable converting between all three formats.

Simplifying ratios is a fundamental skill. Just as you simplify fractions by dividing the numerator and denominator by their greatest common factor, you simplify ratios by dividing all parts by their highest common factor. The ratio 12:8 simplifies to 3:2 when you divide both sides by 4. The ratio 15:25:10 simplifies to 3:5:2 when you divide all three parts by 5. Simplified ratios are easier to work with and less prone to calculation errors under time pressure.

Employers like Unilever and Google include ratio questions in their numerical reasoning assessments because proportional reasoning is essential in business contexts. Budget allocation, resource distribution, market share analysis, and financial forecasting all depend on understanding how quantities relate to one another. By testing ratios, employers evaluate whether you can think proportionally, which is a skill that transfers directly to workplace decision-making.

Types of Ratio Questions in Numerical Reasoning Tests

Ratio questions in aptitude tests come in several distinct formats. Recognising which type you are facing allows you to select the right method immediately, saving valuable time during a timed assessment.

Here is an overview of the main ratio question types and where they commonly appear:

Question Type	What It Asks	Method	Common Providers
Dividing a quantity	Split a total into parts based on a given ratio	Add ratio parts, divide total by sum, multiply each part	SHL, Cubiks/Talogy, Kenexa
Finding a missing value	Given one part of a ratio, find another	Calculate the value of one share, then multiply	SHL, Aon/cut-e
Simplifying ratios	Express given quantities as a ratio in simplest form	Find HCF, divide all parts	Cubiks/Talogy, Kenexa
Ratio to percentage	Convert a ratio into percentage shares	Each part divided by total, multiply by 100	SHL, Aon/cut-e
Changing ratios	A ratio changes when a quantity is added or removed	Set up the new ratio equation and solve	SHL, Cubiks/Talogy
Combining ratios	Merge two related ratios into a single three-part ratio	Find a common term and scale accordingly	SHL, Aon/cut-e
Ratio in data interpretation	Extract values from charts or tables and calculate ratios	Read data accurately, then apply ratio methods	All major providers

Each of these question types builds on the same foundational concept, but the complexity increases as you move from straightforward division to multi-step problems involving changing ratios or data interpretation. The sections below cover each type in detail with worked examples.

If you are also preparing for other question types in numerical reasoning, you may find it helpful to review percentage and fraction calculations alongside ratio practice, since many test questions combine these topics.

Dividing a Quantity in a Given Ratio

This is the most common type of ratio question in aptitude tests. You are given a total amount and a ratio, and you need to split the total according to that ratio.

The method has three steps. First, add up all the parts of the ratio to find the total number of shares. Second, divide the total quantity by the number of shares to find the value of one share. Third, multiply each part of the ratio by the value of one share.

Example 1: A company allocates a training budget of 45,000 pounds between its London and Manchester offices in the ratio 5:4. How much does each office receive?

Step 1: Total shares = 5 + 4 = 9. Step 2: Value of one share = 45,000 / 9 = 5,000. Step 3: London receives 5 x 5,000 = 25,000 pounds. Manchester receives 4 x 5,000 = 20,000 pounds.

Check: 25,000 + 20,000 = 45,000. The answer is correct.

Example 2: A project team of 84 people is divided between three departments in the ratio 2:3:7. How many people are in each department?

Step 1: Total shares = 2 + 3 + 7 = 12. Step 2: Value of one share = 84 / 12 = 7. Step 3: Department A = 2 x 7 = 14. Department B = 3 x 7 = 21. Department C = 7 x 7 = 49.

Check: 14 + 21 + 49 = 84. The answer is correct.

Always perform a quick check by adding your answers together to confirm they equal the original total. This takes only a few seconds and catches arithmetic errors before you submit your answer.

Example 3 (multi-step): Deloitte distributes a bonus pool of 360,000 pounds among partners, senior managers, and associates in the ratio 8:5:2. The associate share is then split equally among 12 associates. How much does each associate receive?

Step 1: Total shares = 8 + 5 + 2 = 15. Step 2: Value of one share = 360,000 / 15 = 24,000. Step 3: Associate total = 2 x 24,000 = 48,000. Step 4: Each associate receives 48,000 / 12 = 4,000 pounds.

This kind of multi-step problem is typical of SHL and Cubiks numerical reasoning tests, where you need to apply a ratio and then perform an additional calculation with the result.

Finding Missing Values Using Ratios and Proportions

When you know the ratio and one actual value, you can find any other value in the ratio. This relies on the concept of proportion, where two ratios are set equal to each other.

Method 1: The unitary method. Find the value of one share first, then multiply.

If A:B = 3:5 and A = 27, then one share = 27 / 3 = 9, so B = 5 x 9 = 45.

Method 2: Cross-multiplication. Set up the proportion as a fraction equation and solve.

If A:B = 3:5 and A = 27, then 3/5 = 27/B. Cross-multiply: 3B = 135, so B = 45.

Both methods give the same answer. The unitary method is usually faster for simple ratios, while cross-multiplication is more reliable for complex problems where you might lose track of which value belongs to which part.

Example: The ratio of male to female applicants at a JP Morgan assessment centre is 7:5. If there are 35 male applicants, how many female applicants are there?

Using the unitary method: One share = 35 / 7 = 5. Female applicants = 5 x 5 = 25.

Example with three parts: In a Civil Service fast-stream intake, the ratio of applicants from humanities, sciences, and other backgrounds is 4:3:2. If 120 applicants come from humanities, how many come from science backgrounds?

One share = 120 / 4 = 30. Science applicants = 3 x 30 = 90.

Notice that you do not need to calculate the total or the third group unless the question asks for it. Focus on the relationship between the parts you need, and ignore information that is not relevant to the specific question being asked.

Practise solving missing-value problems with timed numerical reasoning tests that mirror the format used by major employers.

Ratios and Percentages: Converting Between Formats

Many aptitude test questions require you to switch between ratios and percentages. This is especially common in data interpretation questions where a chart presents data in one format and the question asks for an answer in another.

Converting a ratio to percentages: Add all parts of the ratio to find the total. Then express each part as a fraction of the total and multiply by 100.

For the ratio 3:2, the total is 5. The first part is 3/5 = 60 percent. The second part is 2/5 = 40 percent.

For the ratio 1:2:5, the total is 8. The parts represent 12.5 percent, 25 percent, and 62.5 percent respectively.

Converting percentages to a ratio: Express each percentage as a fraction with a common denominator, then simplify.

If Department A has 40 percent of the budget and Department B has 60 percent, the ratio is 40:60, which simplifies to 2:3.

If three products account for 25 percent, 35 percent, and 40 percent of sales, the ratio is 25:35:40, which simplifies to 5:7:8.

Example: A Unilever market research report shows that Brand X holds 30 percent of the market and Brand Y holds 45 percent. What is the ratio of Brand X's market share to Brand Y's?

The ratio is 30:45. Dividing both by 15 gives 2:3.

Example involving data interpretation: A table shows that Google's advertising revenue is 180 billion dollars and its cloud revenue is 30 billion dollars. What is the ratio of advertising revenue to cloud revenue?

The ratio is 180:30. Dividing both by 30 gives 6:1. This means advertising revenue is six times the cloud revenue.

Understanding the connection between ratios and percentages is particularly valuable because many graph and chart interpretation questions present data as percentages but require you to reason about proportional relationships.

Changing Ratios: When Quantities Are Added or Removed

Some of the most challenging ratio questions in aptitude tests involve ratios that change when a quantity is added to or removed from one part. These questions require you to set up equations and solve for unknowns.

Example: A team currently has men and women in the ratio 3:2. If 4 more women join the team and the ratio becomes 3:4, how many men are on the team?

Let the number of men = 3x and the number of women = 2x (using the original ratio).

After 4 women join: men = 3x, women = 2x + 4.

The new ratio is 3:4, so 3x / (2x + 4) = 3/4.

Cross-multiply: 4(3x) = 3(2x + 4), giving 12x = 6x + 12, so 6x = 12 and x = 2.

Number of men = 3 x 2 = 6.

Check: Originally 6 men and 4 women (ratio 6:4 = 3:2). After adding 4 women: 6 men and 8 women (ratio 6:8 = 3:4). Correct.

Example: A Civil Service department has senior and junior staff in the ratio 2:7. After 15 junior staff members are promoted to senior positions, the ratio becomes 1:2. How many staff are there in total?

Let senior = 2x, junior = 7x.

After promotions: senior = 2x + 15, junior = 7x - 15.

New ratio: (2x + 15) / (7x - 15) = 1/2.

Cross-multiply: 2(2x + 15) = 1(7x - 15), giving 4x + 30 = 7x - 15, so 45 = 3x and x = 15.

Total staff = 2(15) + 7(15) = 30 + 105 = 135.

Check: Originally 30 senior and 105 junior (ratio 30:105 = 2:7). After promotions: 45 senior and 90 junior (ratio 45:90 = 1:2). Correct.

These problems test your algebraic thinking alongside your ratio skills. The key is to express the original quantities using the ratio and a variable, then write an equation based on the changed situation.

Combining Ratios and Multi-Step Problems

When a question gives you two separate ratios that share a common term, you may need to combine them into a single ratio. This is a technique that appears in more advanced numerical reasoning tests, particularly those used by employers like Deloitte, JP Morgan, and Google.

Example: In a company, the ratio of managers to team leads is 2:5, and the ratio of team leads to analysts is 3:7. What is the ratio of managers to team leads to analysts?

The common term is team leads. In the first ratio, team leads = 5. In the second ratio, team leads = 3. To combine, you need team leads to be the same number in both ratios. The lowest common multiple of 5 and 3 is 15.

Scale the first ratio: 2:5 becomes 6:15 (multiply by 3). Scale the second ratio: 3:7 becomes 15:35 (multiply by 5).

Combined ratio: managers : team leads : analysts = 6:15:35.

Example with a total: Using the combined ratio above, if the company has 224 employees in these three roles, how many are analysts?

Total shares = 6 + 15 + 35 = 56. One share = 224 / 56 = 4. Analysts = 35 x 4 = 140.

Multi-step problems often combine ratios with other numerical concepts. You might need to apply a ratio, convert to a percentage, and then calculate a monetary value. The key to handling these problems efficiently is to work through each step methodically and keep your working tidy. Under time pressure, messy working leads to errors that cost you marks.

If you want to sharpen your ability to handle complex multi-step numerical problems, explore multi-step numerical reasoning practice for additional worked examples and strategies.

Common Mistakes and How to Avoid Them

Understanding the typical errors candidates make on ratio questions helps you avoid falling into the same traps during your assessment. Here are the most frequent mistakes and how to prevent them.

Mistake 1: Confusing the ratio with the actual values. A ratio of 3:2 does not mean there are 3 and 2 of something. It means the quantities are in the proportion 3 to 2. The actual values could be 30 and 20, or 300 and 200, or any pair with the same relative size.

Mistake 2: Forgetting to add all parts before dividing. When splitting 500 in the ratio 2:3, some candidates divide 500 by 2 to get the first part. The correct approach is to divide 500 by 5 (the sum of 2 and 3) to find one share, then multiply.

Mistake 3: Writing the ratio in the wrong order. If a question asks for the ratio of sales to costs, and sales are 400 and costs are 600, the ratio is 400:600 = 2:3, not 3:2. Always match the order in the question.

Mistake 4: Not simplifying fully. The ratio 12:18 simplifies to 2:3, not 6:9. Always check whether your simplified ratio can be reduced further.

Mistake 5: Mishandling decimal ratios. If you encounter 0.5:1.5, multiply both parts by 2 to get 1:3. If the ratio is 2.4:3.6, multiply both by 10 to get 24:36, then simplify to 2:3. Always convert to whole numbers before simplifying.

Mistake 6: Rushing through the checking step. After calculating your answer, spend five seconds verifying it. Do the parts add up to the total? Is the ratio between your answers the same as the given ratio? This simple check catches most arithmetic errors.

For a broader look at numerical reasoning errors and how to avoid them, read common numerical reasoning mistakes for advice that applies across all question types.

How Top Employers Use Ratio Questions in Their Assessments

Different employers integrate ratio questions into their recruitment process in different ways. Understanding what to expect from your specific employer helps you target your preparation effectively.

Google uses bespoke numerical reasoning assessments that emphasise data interpretation. Ratio questions at Google typically involve reading data from complex charts and calculating proportional relationships. The questions are timed strictly, and the data sets can be dense, so speed and accuracy with ratios are essential.

Deloitte uses SHL-style numerical reasoning tests as part of its graduate and experienced-hire recruitment. Ratio questions often appear within business-context scenarios, such as splitting revenue between divisions or calculating cost allocations. Deloitte's assessments tend to feature multi-step problems where ratio calculations are one component of a larger question.

Unilever has adopted a digital-first recruitment process that includes numerical reasoning assessments. Their tests frequently feature market share and product distribution scenarios where understanding ratios is critical. Candidates may need to compare brand performance ratios across different markets or time periods.

JP Morgan includes quantitative reasoning in its assessment process, particularly for finance and technology roles. Ratio questions in JP Morgan assessments often involve financial metrics, such as debt-to-equity ratios, price-to-earnings ratios, or the allocation of investment funds across portfolios. Familiarity with financial ratio terminology gives you an edge.

Civil Service fast-stream assessments use numerical reasoning tests that include ratio questions within policy-relevant contexts. You might calculate how government funding is distributed between regions or how staffing ratios compare across departments. The Civil Service tests are known for requiring careful reading of complex data tables.

Regardless of the employer, the mathematical skills you need are the same. What changes is the context and complexity of the scenarios. Practise with a variety of question contexts so that no scenario feels unfamiliar on test day.

Strategies for Solving Ratio Questions Under Time Pressure

Time management is critical in numerical reasoning tests. Most assessments allow between 60 and 90 seconds per question, and ratio questions can range from quick calculations to complex multi-step problems. Here are strategies to help you work efficiently.

Read the question twice before calculating. Many errors come from misunderstanding what the question is asking. Spending five extra seconds reading carefully can save you from a wrong answer that wastes 60 seconds.

Simplify early. If the question gives you the ratio 24:36, simplify to 2:3 before doing any calculations. Working with smaller numbers reduces the chance of arithmetic errors and speeds up your mental maths.

Use estimation to check your answer. If you split 1,000 in the ratio 2:3, the larger part should be roughly 600. If your calculation gives you 400, something has gone wrong. Quick estimation catches errors without requiring a full recalculation.

Know when to skip. If a ratio question involves multiple steps and you are running low on time, it may be better to move on to a simpler question and return to the complex one if time permits. Most aptitude tests do not penalise unanswered questions more heavily than wrong answers.

Practise mental arithmetic. The faster you can divide and multiply without a calculator, the more time you have for reading data and checking your work. Practice dividing by common numbers like 3, 4, 5, 7, and 8 until it becomes automatic.

Write down intermediate values. Even if you are confident in your mental arithmetic, writing down intermediate steps prevents you from losing track mid-calculation. This is especially important for three-part ratios and multi-step problems.

Build your speed and accuracy with realistic practice tests that replicate the time pressure and question formats used by top employers.

Frequently Asked Questions

What is the difference between a ratio and a proportion?

A ratio compares two or more quantities by showing their relative sizes. For example, 2:3 tells you that the first quantity is two-thirds the size of the second. A proportion is a mathematical statement that two ratios are equal. For example, 2/3 = 4/6 is a proportion because both fractions represent the same relative size. In aptitude tests, ratio questions ask you to compare, divide, or simplify quantities, while proportion questions typically require you to find a missing value when two ratios are set equal. Both concepts appear regularly in numerical reasoning assessments from providers like SHL and Cubiks/Talogy, and understanding the distinction helps you identify the correct solution method quickly.

How do I solve ratio questions with more than two parts?

The method is identical to two-part ratios. Start by adding all the parts of the ratio together to find the total number of shares. Then divide the total quantity by that sum to find the value of one share. Finally, multiply each ratio component by the value of one share to find the actual amount for each part. For example, if you need to split 600 in the ratio 2:3:5, the total parts equal 10. One share equals 600 divided by 10, which is 60. The three portions are 120, 180, and 300. Always verify by adding the portions to confirm they equal the original total.

Can ratios contain decimals or fractions?

Ratios are typically expressed as whole numbers in aptitude tests, but you may occasionally encounter decimal or fractional ratios. To handle them, multiply every part of the ratio by the same factor to eliminate the decimals or fractions. For instance, the ratio 1.5:2 becomes 3:4 when you multiply both sides by 2. The ratio 1/3:1/2 becomes 2:3 when you multiply both sides by 6. The goal is to convert to whole numbers as quickly as possible, since whole-number ratios are much easier to work with under time pressure.

How do I convert a ratio into a percentage?

Add up all parts of the ratio to find the total number of shares. Then divide each individual part by the total and multiply by 100 to get the percentage. For a ratio of 3:7, the total is 10. The first part represents 3/10, or 30 percent, and the second part represents 7/10, or 70 percent. For a three-part ratio like 1:3:6, the total is 10, giving percentages of 10, 30, and 60 percent. This conversion is especially useful when aptitude test questions present data as ratios in one part of the question and ask for answers as percentages, or vice versa.

What types of ratio questions appear in SHL and Cubiks numerical tests?

SHL and Cubiks numerical reasoning tests typically embed ratio questions within data interpretation scenarios. Rather than presenting a straightforward ratio to simplify, these tests require you to extract figures from tables, bar charts, or pie charts and then calculate a ratio from the data. Common scenarios include splitting budgets between departments, comparing regional sales figures, calculating ingredient proportions in manufacturing, or determining how market share is distributed among competitors. The data may involve multiple steps, such as calculating a ratio from the data and then using that ratio to project a future value.

How much time should I spend on a ratio question during an aptitude test?

Most numerical reasoning tests allow between 60 and 90 seconds per question. Simple ratio questions involving straightforward division or simplification can often be solved in 30 to 45 seconds, leaving time for a quick check. However, multi-step problems that combine ratios with percentages, currency conversions, or data extraction from charts may require the full time allowance or even longer. The best approach is to practise under timed conditions so you develop an instinct for pacing. If a question is taking significantly longer than 90 seconds, consider marking it and moving on to earn points on easier questions first.

Start Preparing for Ratio Questions Today

Ratio questions are a core component of numerical reasoning tests used by employers like Google, Deloitte, Unilever, JP Morgan, and the Civil Service. The mathematical concepts behind these questions are not difficult, but performing accurately under strict time pressure requires practice. Candidates who invest time in structured preparation consistently outperform those who rely on their general maths ability alone.

The most effective way to prepare is to work through realistic practice questions that mirror the format, difficulty, and time constraints of real assessments. Focus on building both your accuracy and your speed, and pay particular attention to multi-step problems and data interpretation scenarios where ratios are combined with other numerical concepts.

Get started with the complete test package at assessment-training.com to access practice tests covering SHL, Cubiks/Talogy, Kenexa, Aon, and other major providers. Build the skills and confidence you need to handle every ratio question your assessment throws at you.