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Reverse percentages practice questions with answers

Foundation and Higher · Grade 5

A second set of reverse percentages questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

After a 50% decrease the price is £30. Work out the original price.

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Answer: 60

  1. Remaining is 50%, multiplier is 0.5.
  2. Divide: 30 / 0.5 = 60.
  • Method (1): Remaining is 50%, multiplier is 0.5.
  • Accuracy (1): Divide: 30 / 0.5 = 60.

Question 2 Easy

After a 20% decrease the price is £40. Work out the original price.

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Answer: 50

  1. Remaining is 80%, multiplier is 0.8.
  2. Divide: 40 / 0.8 = 50.
  • Method (1): Remaining is 80%, multiplier is 0.8.
  • Accuracy (1): Divide: 40 / 0.8 = 50.

Question 3 Medium

After a 10% increase the price is £33. Work out the original price.

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Answer: 30

  1. New amount is 110%, multiplier is 1.1.
  2. Divide: 33 / 1.1 = 30.
  • Method (1): New amount is 110%, multiplier is 1.1.
  • Accuracy (1): Divide: 33 / 1.1 = 30.

Question 4 Medium

After a 50% increase the price is £45. Work out the original price.

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Answer: 30

  1. New amount is 150%, multiplier is 1.5.
  2. Divide: 45 / 1.5 = 30.
  • Method (1): New amount is 150%, multiplier is 1.5.
  • Accuracy (1): Divide: 45 / 1.5 = 30.

Question 5 Hard

A price falls from £50 to £40. Work out the percentage decrease.

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Answer: 20

  1. Difference is 50 - 40 = 10.
  2. Percentage drop: (10 / 50) × 100 = 20.
  • Method (1): Difference is 50 - 40 = 10.
  • Accuracy (1): Percentage drop: (10 / 50) × 100 = 20.

Question 6 Hard

A price falls from £80 to £60. Work out the percentage decrease.

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Answer: 25

  1. Difference is 80 - 60 = 20.
  2. Percentage drop: (20 / 80) × 100 = 25.
  • Method (1): Difference is 80 - 60 = 20.
  • Accuracy (1): Percentage drop: (20 / 80) × 100 = 25.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 13 marks

A price falls from £250 to £175. Work out the percentage decrease.

Show answer

Answer: 30

  1. Calculate the drop: 250 - 175 = 75.
  2. Divide by original: 75 / 250 = 0.3.
  3. Multiply by 100: 0.3 × 100 = 30%.
  • Method (1): Find drop: 250 - 175 = 75
  • Method (1): 75 ÷ 250 × 100
  • Accuracy (1): 30%

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

To find the original price after a decrease, what do you do?

  1. Divide by the decrease multiplier
  2. Add the percentage back
  3. Multiply by the decrease multiplier
Show answer

Divide by the decrease multiplier Divide by the multiplier (which is less than 1).

Check 2

After a 20% decrease the price is £80. What was the original price?

  1. £100
  2. £96
  3. £64
Show answer

£100 80 ÷ 0.8 = 100.

Check 3

After a 25% decrease the price is £60. What was the original price?

  1. £80
  2. £75
  3. £45
Show answer

£80 60 ÷ 0.75 = 80.

Check 4

After a 10% increase the price is £66. What was the original price?

  1. £60
  2. £59.40
  3. £72.60
Show answer

£60 66 ÷ 1.1 = 60.

Check 5

After a 20% increase the price is £72. What was the original price?

  1. £60
  2. £86.40
  3. £57.60
Show answer

£60 72 ÷ 1.2 = 60.

Check 6

What is the multiplier for a 20% decrease?

  1. 0.8
  2. 1.2
  3. 0.2
Show answer

0.8 100% - 20% = 80% = 0.8.

Check 7

What is the multiplier for a 10% increase?

  1. 1.1
  2. 0.1
  3. 1.01
Show answer

1.1 100% + 10% = 110% = 1.1.

Check 8

What is the multiplier for a 25% increase?

  1. 1.25
  2. 0.25
  3. 0.75
Show answer

1.25 100% + 25% = 125% = 1.25.

Check 9

A price decreases from 100 to 80. What is the percentage decrease?

  1. 20%
  2. 80%
  3. 25%
Show answer

20% (20 / 100) × 100 = 20%.

Check 10

A price decreases from 50 to 40. What is the percentage decrease?

  1. 20%
  2. 10%
  3. 25%
Show answer

20% (10 / 50) × 100 = 20%.

Check 11

Why does adding 20% to a sale price not restore the original price?

  1. The sale price is smaller than the original
  2. Percentages cannot be added
  3. The multiplier was wrong
Show answer

The sale price is smaller than the original 20% of a smaller number is less than 20% of the larger original.

Check 12

If 20% is lost, what decimal multiplier gives the price that remains?

  1. 0.8
  2. 0.2
  3. 1.2
Show answer

0.8 1 - 0.2 = 0.8.

Check 13

A 50% decrease halves a price. How do you find the original?

  1. Double the sale price
  2. Subtract half
  3. Divide by 2
Show answer

Double the sale price Dividing by 0.5 is multiplying by 2.

Check 14

What is the multiplier for a 5% increase?

  1. 1.05
  2. 1.5
  3. 0.95
Show answer

1.05 100% + 5% = 105% = 1.05.

Check 15

How do you calculate percentage change between two amounts?

  1. (Change ÷ Original) × 100
  2. (Original ÷ Change) × 100
  3. (New ÷ Old) × 100
Show answer

(Change ÷ Original) × 100 Percentage change is always relative to the original amount.

Keep going with Reverse percentages

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