GCSE · Ratio

Ratio problems where the amounts changeExam-style questions

How to handle ratios where quantities are added, removed or transferred by writing the parts as multiples of a common number and solving for it.

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

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
In a box, the ratio of red beads to blue beads is 3 : 4. When 6 more red beads are added to the box, the ratio of red beads to blue beads becomes 9 : 8. Work out the original number of blue beads.
Level 5 · 4 marksTry it
2
Jar A and Jar B contain marbles in the ratio 5 : 3. When 8 marbles are moved from Jar A to Jar B, the two jars then contain marbles in the ratio 1 : 1. Work out how many marbles were in Jar A to begin with.
Level 5 · 4 marksTry it
3
In a drawer, the ratio of pens to pencils is $2 : 5$ .

When $9$ more pens are put in the drawer, the numbers of pens and pencils become equal.

Work out the total number of items in the drawer after the pens are added.
Level 5 · 3 marksTry it
4
Two boxes, $A$ and $B$ , contain counters in the ratio $7 : 3$ .

When $12$ counters are moved from box $A$ to box $B$ , the two boxes contain equal numbers.

Work out the total number of counters.
Level 5 · 3 marksTry it