# Finding the Original Quantity After a Percentage Increase or Decrease

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

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Define, Interpret and Compare Percentages

Difficulty level:

### 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.

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?

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.

If the question is about money, remember to give you answer to 2 decimal places (Pounds and pence) unless it is a whole number.

A coat costs £250 in a 20% off sale. Find the price of the coat before it was reduced.

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

A coat costs £250 in a 20% off sale. Find the price of the coat before it was reduced.

437.50
EDDIE SAYS
20% off means that 80% of the original value is left. 80% = 0.8 Original price x 0.8 = 350 £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.

200
EDDIE SAYS
20% more represents 120% of the original value. 120% = 1.2 Original x 1.2 = 240 240 ÷ 1.2 = 200
• Question 3

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

284
EDDIE SAYS
25% increase represents 125% of the original value. 125% = 1.25 Original x 1.25 = 355 355 ÷ 1.25 = 284
• Question 4

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

470
EDDIE SAYS
10% off represents 90% of the original value. 90% = 0.9 Original x 0.9 = 423 £423 ÷ 0.9 = £470
• Question 5

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

500
EDDIE SAYS
6% reduction represents 94% of the original value. 94% = 0.94 Original x 0.94 = 470 470 ÷ 0.94 = 500
• Question 6

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

460
EDDIE SAYS
15% increase represents 115% of the original value. 115% = 1.15 Original x 1.15 = 529 529 ÷ 1.15 = 460
• Question 7

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

352
EDDIE SAYS
25% increase represents 125% of the original value. 125% = 1.25 Original x 1.25 = 440 440 ÷ 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

250
EDDIE SAYS
A reduction of 11% represents 89% of the original value. 89% = 0.89 Original x 0.89 = 222.50 £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?

300
EDDIE SAYS
30% increase represents 130% of the original value. 130% = 1.3 Original x 1.3 = 390 390 ÷ 1.3 = 300
• Question 10

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

425
EDDIE SAYS
12% increase represents 112% of the original value. 112% = 1.12 Original x 1.12 = 476 476 ÷ 1.12 = 425
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