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Finding the Original Quantity After a Percentage Increase or Decrease

In this worksheet, students find the original quantity after a percentage increase/decrease.

'Finding the Original Quantity After a Percentage Increase or Decrease' worksheet

Key stage:  KS 3

Curriculum topic:  Number

Curriculum subtopic:  Define, Interpret and Compare Percentages

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

This worksheet 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.

 

Answer


80% of original price = £65.

0.8 × original price = £65.

Original price = £65 ÷ 0.8 = £81.25

 


Example 2


A sum of money is deposited in a bank account paying 6% interest per annum (every year). After one year there is £1113 in the account. How much money was deposited?

 

Answer

106% of original sum = £1113.


1.06 × original sum = £1113.

Original sum deposited = £1113 ÷ 1.06 = £1050

 

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

Find the original price of goods, sold for £350 after a 20% reduction in a sale.

There were 240 people at a restaurant this evening.  This is 20% more than there were at lunchtime.  Find out how many there were at lunchtime.

Find the original quantity which becomes 355 after an increase of 25%.

Find the original price of goods in a "10% off" sale, when the sale price is £423.

A number becomes 470 after a 6% reduction.  What was the original number?

Find the original quantity which becomes 529 after an increase of 15%.

Find the original quantity which becomes 440 after an increase of 25%.

Find the original price of goods in a sale after a reduction of 11% when the sale price is £222.50

After increasing quantities by 30%, a chef needs to order 390 eggs.  How many eggs would he have ordered before the increase?

Find the original quantity which becomes 476 after an increase of 12%.

  • Question 1

Find the original price of goods, sold for £350 after a 20% reduction in a sale.

CORRECT ANSWER
£437.50
£ 437.50
EDDIE SAYS
£350 ÷ 0.8 = £437.50
  • Question 2

There were 240 people at a restaurant this evening.  This is 20% more than there were at lunchtime.  Find out how many there were at lunchtime.

CORRECT ANSWER
200
EDDIE SAYS
240 ÷ 1.2 = 200
  • Question 3

Find the original quantity which becomes 355 after an increase of 25%.

CORRECT ANSWER
284
EDDIE SAYS
355 ÷ 1.25 = 284
  • Question 4

Find the original price of goods in a "10% off" sale, when the sale price is £423.

CORRECT ANSWER
£470
£ 470
EDDIE SAYS
£423 ÷ 0.9 = £470
  • Question 5

A number becomes 470 after a 6% reduction.  What was the original number?

CORRECT ANSWER
500
EDDIE SAYS
470 ÷ 0.94 = 500
  • Question 6

Find the original quantity which becomes 529 after an increase of 15%.

CORRECT ANSWER
460
EDDIE SAYS
529 ÷ 1.15 = 460
  • Question 7

Find the original quantity which becomes 440 after an increase of 25%.

CORRECT ANSWER
352
EDDIE SAYS
440 ÷ 1.25 = 352
  • Question 8

Find the original price of goods in a sale after a reduction of 11% when the sale price is £222.50

CORRECT ANSWER
£250
£ 250
EDDIE SAYS
£222.50 ÷ 0.89 = £250
  • Question 9

After increasing quantities by 30%, a chef needs to order 390 eggs.  How many eggs would he have ordered before the increase?

CORRECT ANSWER
300
EDDIE SAYS
390 ÷ 1.3 = 300
  • Question 10

Find the original quantity which becomes 476 after an increase of 12%.

CORRECT ANSWER
425
EDDIE SAYS
476 ÷ 1.12 = 425
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