Ratio Problem Solving in Context –

Ratio problem solving in context is a staple of GCSE Maths exams across all boards. These questions wrap ratio skills into real-world scenarios — recipes, best-value shopping, mixing paint, sharing money, and more. They test whether you can extract the ratio from the context, identify what you are solving for, and apply the right method. Many students find these questions tricky because the maths is hidden inside words. This guide gives you a reliable approach for tackling any ratio problem in context, with fully worked examples at Foundation and Higher level.

What Is Ratio Problem Solving in Context?

Ratio problem solving takes the core ideas of ratio — comparing, sharing and scaling — and applies them to everyday situations. The key skill is translating the words into a ratio and then using standard methods to find the answer.

Common contexts

• Recipes: scaling ingredients up or down for a different number of servings.
• Best buys: comparing prices per unit to find the cheapest option.
• Mixing: combining quantities in a given ratio (e.g., paint, drinks, concrete).
• Maps and scale drawings: using a ratio to convert between a drawing and real life.
• Combined ratios: linking two separate ratios that share a common quantity.

Key principle

If two quantities are in the ratio a : b, then:

You can use this to set up and solve equations when one quantity is known.

Step-by-Step Method

General approach to contextual ratio problems

1. Read the question carefully — identify the quantities and the ratio connecting them.
2. Write the ratio down and label each part clearly (e.g., flour : sugar = 3 : 2).
3. Identify what you know and what you need to find.
4. Find the value of one part or use a multiplier to scale the ratio.
5. Calculate the answer and include appropriate units.
6. Check your answer makes sense in context.

Scaling a recipe

1. Find how many times bigger (or smaller) the new quantity is compared to the original for the ingredient you know.
2. Multiply all other ingredients by the same scale factor.

Best-buy problems

1. Find the price per unit (e.g., price per gram or price per litre) for each option.
2. Compare the unit prices — the lowest unit price is the best value.

Worked Example 1 — Foundation Level (Recipe)

Question: A recipe for 12 biscuits uses 200 g flour, 100 g butter and 80 g sugar. How much of each ingredient is needed for 30 biscuits?

Step 1: Find the scale factor: 30 ÷ 12 = 2.5

Step 2: Multiply each ingredient by 2.5:

• Flour: 200 × 2.5 = 500 g
• Butter: 100 × 2.5 = 250 g
• Sugar: 80 × 2.5 = 200 g

Check: 30 is 2.5 times 12, and each ingredient is 2.5 times the original ✓

Worked Example 2 — Higher Level (Combined Ratios)

Question: In a class, the ratio of boys to girls is 3 : 4. The ratio of girls who wear glasses to girls who do not is 1 : 3. There are 28 students in the class. How many girls wear glasses?

Step 1: Boys : Girls = 3 : 4. Total parts = 7.

Step 2: Number of girls = (4/7) × 28 = 16.

Step 3: Girls with glasses : Girls without = 1 : 3. Total parts = 4.

Step 4: Girls who wear glasses = (1/4) × 16 = 4.

Check: Boys = 12, Girls without glasses = 12, Girls with glasses = 4. Total = 28 ✓

Common Mistakes

• Not reading which way the ratio goes. "The ratio of A to B is 3 : 5" means A has 3 parts and B has 5. Reversing these gives the wrong answer.
• Mixing up total and difference. If you are told the total is 240, divide by the sum of the parts. If you are told the difference is 24, divide by the difference of the parts.
• Forgetting units in best-buy questions. You must compare like with like. If one price is per 100 g and another is per kg, convert before comparing.
• Not simplifying before scaling. Simplifying the ratio first can make the calculation much easier, especially with large numbers.
• Rounding too early in best-buy calculations. Work out the exact price per unit before comparing, or you may choose the wrong option.

Exam Tips

1. Show your scale factor. In recipe questions, write "scale factor = 30 ÷ 12 = 2.5" explicitly. This earns a method mark even if you make an arithmetic slip later.
2. For best-buy questions on Edexcel and OCR, you are often asked "Which is better value? You must show your working." Simply circling an answer without calculation scores zero.
3. When ratios share a common quantity, rewrite both ratios so that the shared quantity has the same number in both. For example, A : B = 2 : 3 and B : C = 6 : 5. Rewrite the first as A : B = 4 : 6, so the combined ratio is A : B : C = 4 : 6 : 5.
4. Draw a bar model if you find the problem hard to visualise. Bar models are an excellent way to represent ratio problems and many students find them helpful in exams.

Practice Questions

Question 1 (Foundation): A bag contains red and blue sweets in the ratio 2 : 5. There are 35 sweets in total. How many are red?

Question 2 (Foundation): Pack A contains 500 ml of juice for £1.20. Pack B contains 1.5 litres for £3.00. Which is better value?

Question 3 (Higher): The ratio of Tom's age to Sam's age is 5 : 3. In 4 years' time, the ratio will be 3 : 2. Find their current ages.

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Related Topics

• Ratio Basics and Sharing
• Direct and Inverse Proportion
• Percentages: Increase and Decrease
• Speed, Distance and Time

Summary

• Ratio problem solving applies ratio skills to real-world contexts such as recipes, best buys and maps.
• Always identify the ratio from the wording and label each part clearly.
• For recipe scaling, find the scale factor and multiply all ingredients by it.
• For best-buy problems, calculate the price per unit for each option and compare.
• To combine two ratios, make the shared quantity equal in both ratios before merging.
• Show all working clearly — method marks are available for each step.
• Always check your answer makes sense in the context of the question.