Sheet № 34 · Foundation + Higher · AQA · Edexcel · OCR
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.
§Key definitions
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:
Check:
30 is 2.5 times 12, and each ingredient is 2.5 times the original ✓
Step 3:
Girls with glasses : Girls without = 1 : 3. Total parts = 4.
§Formulas to memorise
quantity₁ / quantity₂ = a / b
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.
Read the question carefully — identify the quantities and the ratio connecting them.
Write the ratio down — and label each part clearly (e.g., flour : sugar = 3 : 2).
Identify what you know — and what you need to find.
Find the value of one part — or use a multiplier to scale the ratio.
Worked example
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
⚠ 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
- →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.
- →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.
- →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.
- →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.
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