Ratio and Proportion in the 11+ — Questions, Worked Answers and Practice Papers
Sharing quantities in a ratio, scaling recipes and maps, and solving proportion problems in the 11+.
29Papers
2.1Avg Qs / paper
1.64Typical marks
46 secTarget time
What examiners actually ask
Ratio and Proportion appears in 29 of our 338 ready papers (61 tagged questions). It averages 2.1 questions a paper worth about 1.64 marks each. The typical question allows around 46 sec.
Ratio and proportion questions are fewer than fractions overall, but they punch above their weight in selective papers — especially independent-school Maths. Typical asks: share an amount in a given ratio, find one part when another is known, or scale a recipe or map. Children who treat ratio as two unrelated numbers, or who forget to use all the parts when sharing, drop marks quickly. Teach “parts” language explicitly, bar models for sharing, and unitary method for proportion, then practise under timed conditions. Always write the total number of parts before dividing, and check whether the question wants one share, several shares, or the difference between shares. A thirty-second sense-check (“do the parts add back to the original amount?”) prevents many expensive mistakes.
Worked example
A real tagged question from our catalogue — method included, not paywalled.
The concepts that you must know to solve this question are
1. What is a model? why do you need a model?
2. What is ratio?
3. What is a scale? and what does it mean?
4. What does a scale of 1:50 really mean?
{"text":"bold","word":"What is a model? why do you need a model?"}
A model is a 3D representation of a real thing. Before you make the real thing you make a model so that you know exactly how it will look like and also show it to people and workers before the real thing is made.
{"text":"bold","word":"What is a ratio?"}
It is a comparison of two things. It can be a comparison of men to women, apples to oranges, iPhone to Android or any two things.
{"text":"bold","word":"What is a scale? and what does it mean?"}
A scale is a comparison of real life sizes to the size on a drawing or model. Example, a map shows a drawing of the real world but the size of a country on a map is much smaller than the real life, however, it must still represent the reality. The scale tells how many cm on paper really means in reality.
{"text":"bold","word":"What does a scale of 1:50 really mean?"}
It means that 1 cm on the model represents 50 cm in real life. So if something on the model is 1 cm long then in real life it will be 50 cm long.
{"text":"bold","word":"Time to solve the problem"}
The eye-full tower is 120m tall.
Let's first convert this into cm.
1 m = 100 cm, so 120m
= 120 x 100
= 12000 cm
The scale is 1:50. This means that 1cm on the model is equal to 50cm in real life.
In other words, each 50cm in the real life tower will be represented by 1 cm on the model.
Let's divide 12000 cm in to equal portions of 50 cm and find out how many such portions do we get.
= 12000 / 50
= 1200/5
= 12 x 100 / 5
= 12 x 20
= 240
Each 50 cm part will become 1 cm on the model. So 240 parts will become 240 x 1 cm.
= 240 cm
Common mistakes
Sharing an amount into the ratio numbers themselves instead of into the total number of parts.
Finding one part correctly then forgetting to multiply up for the quantity asked.
Confusing ratio order (A:B) when the question asks for B’s share.
Scaling only one quantity in a proportion word problem.
Papers with the most Ratio and Proportion questions
Ranked from our tagged catalogue — open a paper to practise the questions that actually test this topic.
Not sure whether ratio and proportion is the problem? Mark any past paper on 11plusSolved and the report tells you which topics are costing marks — and how many.
