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Find the Original Quantity After a Percentage Change

In this worksheet, students will find original quantities after a percentage increase/decrease.

'Find the Original Quantity After a Percentage Change' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Number

Curriculum subtopic:   Define, Interpret and Compare Percentages

Difficulty level:  

Worksheet Overview

This activity is about finding the original quantity after a percentage increase/decrease has been applied.


Example 1

In a sale, the price of a DVD player, after a 20% reduction, is £65. Find its price before the sale.



80% of original price = £65.

Divide 80% by 100 to remove the percentage = 0.8

0.8 × original price = £65.

Original price = £65 ÷ 0.8 = £81.25


dvd player


Example 2

A sum of money is deposited in a bank account paying 6% interest per annum (every year). After one year there is £1,113 in the account. How much money was deposited?



106% of original sum = £1,113.

Divide 106% by 100 to remove the percentage = 1.06

1.06 × original sum = £1,113.

Original sum deposited = £1,113 ÷ 1.06 = £1,050


ALWAYS CHECK that the sale price is less than the original and that an increased quantity is more than the original!


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In this activity, don't put any units in your answer.

If the question is about money, remember to give your answer to 2 decimal places - that is pounds and pence - unless it is a whole number.


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