FRACTIONS, DECIMALS AND PERCENTAGES

Multi Step Percentage Problems

Learn the reliable method for multi step percentage problems, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

In a multi-step percentage problem, each change must be applied to the correct current value.

Picture itConnect parts out of 100
Stationery and UK money arranged as a real-life shopping problem
2 · THE METHOD

Follow these steps

  1. Write the value after each stage.
  2. Apply percentage changes in the stated order.
  3. Complete any fixed additions or subtractions and check the direction of every change.
percentage = amount ÷ 100 × rate
3 · WORKED EXAMPLES

See the method in action

Example 1

Asha scores 28 out of 40; Ben scores 48 out of 80. By how many percentage points is Asha's score higher?

  1. Convert 28/40 and 48/80 to percentages.
  2. Subtract the second percentage from the first.
  3. Therefore the answer is 10 percentage points.
Answer: 10 percentage points
Example 2

A musical instrument costs £80.00. Its price rises by 20% and the new price is then reduced by 25%. What is the final price?

  1. Increase £80.00 by 20%.
  2. Decrease the increased price by 25%; do not apply the reduction to the original price.
  3. Therefore the answer is £72.00.
Answer: £72.00
4 · ELEVENSPRINT TIP

A useful shortcut

Complete any fixed additions or subtractions and check the direction of every change.

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.