Finding the original amount before an increase
You know the price after a rise or a cut and need the price before it. Learn why you divide, and what to divide by.
In this room: 3 tasks, 9 questions
- Working back from an increase4 questions
- Why taking the percentage off is wrong2 questions
- Working back from a decrease3 questions
The original amount is 100% of itself. After a 20% increase, the new amount is 120% of the original.
- Step 1: add the percentage rise to 100, then divide by 100. A 20% rise gives 1.2
- Step 2: divide the new amount by that figure
Worked example: a price is £60 after a 20% rise. 60 ÷ 1.2 = £50. Check: 20% of £50 is £10, and adding it gives £60.
Answer the questions below
3 more questions follow in this task.
It is tempting to take the same percentage off the new price. That gives the wrong answer.
The rise was worked out on the old price. Taking the percentage off the new price works it out on a bigger figure, so it takes off too much.
A sander costs £90 after a rise of 25%. Priya takes 25% off £90 and gets £67.50.
Answer the questions below
1 more question follows in this task.
The same idea works for a price cut. After 20% off, the new price is 80% of the original.
- Step 1: take the percentage cut away from 100, then divide by 100. A 20% cut gives 0.8
- Step 2: divide the new amount by that figure
Worked example: a sale price is £40 after 20% off. 40 ÷ 0.8 = £50.
Answer the questions below
2 more questions follow in this task.