RATIO AND PROPORTION

Ratio Word Problems

Learn the reliable method for ratio word problems, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Ratio word problems link the stated parts to an actual total or difference.

Picture itCompare each group in the same order
Bowls, fruit, scales and a measuring jug showing ratio and measurement in baking
2 · THE METHOD

Follow these steps

  1. Represent each quantity with ratio parts.
  2. Use the total or difference to find one part.
  3. Scale the requested quantity and check the order of the ratio.
one share = total ÷ sum of ratio parts
3 · WORKED EXAMPLES

See the method in action

Example 1

For every blue bead, a necklace has 3 red beads. There are 4 blue beads. How many red beads are there?

  1. Each of the 4 blue beads corresponds to 3 red beads.
  2. There are 4 × 3 = 12 red beads.
Answer: 12
Example 2

The ratio of morning swimmers to evening swimmers is 7:5. There are 20 more morning swimmers than evening swimmers. How many are there altogether?

  1. The difference is 2 ratio parts, so one part is 20 ÷ 2 = 10.
  2. There are 12 parts altogether, giving 12 × 10 = 120.
Answer: 120
4 · ELEVENSPRINT TIP

A useful shortcut

Scale the requested quantity and check the order of the ratio.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.