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Solve Problems Involving Multiple Ratios

In this worksheet, students will solve problems using multiple ratios.

'Solve Problems Involving Multiple Ratios' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Use Ratio Notation

Difficulty level:  

Worksheet Overview

In this activity, we will use what we know about ratio to solve some problems involving multiple ratios.

Previously, we have looked at problems with multiple ratio.



In a jar there are green, red and yellow sweets.

The ratio of green to red is 3:1

The ratio of red to yellow is  2:5

Find the ratio of greenredyellow


boy thinking



Firstly, we cannot just put them together.

They need to be in the same proportions.

That means, the one that links them has to be the same - confused?

Let's do it and it will help


Write them out as we have them:



We need the red to be the same because it is in both ratios.

So if we multiply 3:1 by 2 = 6:2 the two ratios are proportional.



The ratio of green:red:yellow = 6:2:5


Got that?


man thumbs up


Let's move on then, and take what we know from this to this activity.



The points A, B, C and D lie in alphabetical order on a straight line.

AB:BD = 2:3 and AC:CD = 5:6


Find the ratio AB:BC:CD



Draw this straight line out so you can see what is going on.



They need to be in the same proportions.


2:3       ⇒      2 + 3 = 5

5:6       ⇒      5 + 6 = 11

The lowest common multiple here is 55

2:3 (x 11) = 22:33        ⇒      22 + 33 = 55

5:6 (x 5) = 25:30          ⇒    25 + 30 = 55


Now they are in the same proportion, we can change the ratios on the line:



We can see from the diagram that A:B = 22

Therefore, B:C = 25 - 22 = 3

C:D = 30



Final answer;

AB:BC:CD = 22:3:30


worried woman


Don't worry - you won't be the only one who finds these tricky!!

The best way to get them sorted is to practise!


Let's get started. You can look back at this introduction at any point by clicking on the red help button on the screen.

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