GCSE · Ratio

Combining and relating ratiosExam-style questions

How to link two ratios that share a quantity into one three-part ratio, and how ratios connect to fractions and to the "1 : n" form.

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16 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 4 Level 5

1
$5a : 4b = 6 : 7$

$2b : c = 7 : 2$

Show that $a + c : b + c = 4 : 5$

(3 marks)
Level 5 · 3 marksTry it
2
In a company, the ratio of managers to staff is 1 : 8, and the ratio of staff to trainees is 4 : 3. There are 96 staff. Work out the total number of managers, staff and trainees in the company.
Level 5 · 4 marksTry it
3
The ratio $(2x + 1) : (x + 4)$ is equal to the ratio $3 : 2$ . Work out the value of $x$ .
Level 5 · 3 marksTry it
4
The ratio $(3x - 2) : (x + 6)$ is equal to the ratio $5 : 3$

Work out the value of $x$ .
Level 5 · 3 marksTry it
5
$p : q = 2 : 5$ and $q : r = 10 : 7$

$r$ is $12$ more than $p$ .

Work out the value of $q$ .
Level 5 · 4 marksTry it