Unit 8 · Rates and Ratios
Teacher–Pupil Ratio — Scaling Groups
Lesson 1 of 7
Let's start with the most fundamental ratio question type: given a ratio between two quantities, one quantity changes — find the other. The key move is finding how many 'groups' the new total contains, then scaling the other side by that same number of groups.
Ratio and proportion questions appear in every OC MR paper, spread from easy to medium difficulty. The scaling format shown here is the most common variant — it is an easy mark for students who use the unit-groups method and a common error for those who try to cross-multiply fractions under time pressure.
The examiner is checking whether you can identify the matching ratio part (pupils = 25), divide the given total by it to find the number of groups, and then multiply the other ratio part (teachers = 3) by that number — rather than setting up a proportion equation that is slower to solve.
A ratio between two quantities is stated (e.g. 3 teachers : 25 pupils). One quantity is scaled to a new value (1050 pupils). You must find the corresponding value of the other quantity. The total is always chosen to divide exactly by the ratio part, so no decimals are needed.
Best approach: Step 1: Identify which ratio part matches the given total. Step 2: Divide the total by that ratio part to find the number of groups. Step 3: Multiply the other ratio part by the number of groups. Always check: groups × both ratio parts should reproduce the original and the given total.
Question
In a school, there are 3 teachers to every 25 pupils. If there are 1050 pupils, how many teachers are there?
Select an answer to see the explanation.
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