Reverse percentages

The Maths Habit
Walkthrough to print

  1. Increase £60 by 15%

    £69

  2. Decrease £84 by 25%

    £63

  3. An amount is multiplied by 1.08. Is this an increase or a decrease? By what percentage?

    An 8% increase

A price goes up by 20%. Then the new price comes down by 20%. Is it back where it started?

No: it is 4% lower

Reverse percentages

  1. Draw the barsThe original is 100%.
    The amount now is shorter, or longer after an increase.
  2. Percentage nowThe amount now, as a percentage of the original.
  3. Find 1%Divide by the percentage now to find 1%.
  4. Multiply by 100Multiply by 100 to get back to the original.
100% − % off = % now
1% = amount now ÷ % now
100% = 1% × 100
an increase? 100% + the % on
never take the % off the amount now
Walkthrough to print

What percentage of the original is it now?

  1. A 20% increase

    120%

  2. A 15% increase

    115%

  3. A 10% decrease

    90%

  4. A 35% decrease

    65%

After a 30% increase, a price is £91. Find the original price.

original100%?now130%£91
the amount now, as a percentage of the original
130% = £91
divide to find 1%
1% =0.7
multiply by 100
100% =70
Original£70

In a 40% off sale, a lamp costs £45. Find the original price.

original100%?now60%£45
the amount now, as a percentage of the original
60% = £45
divide to find 1%
1% =0.75
multiply by 100
100% =75
Original£75

After a 30% increase, a price is £91. Find the original price.

original100%?now130%£91
the amount now, as a percentage of the original
130% = £91
divide to find 1%
1% =0.7
multiply by 100
100% =70
Original£70

A sofa is reduced by 15% to £340. Find the original price.

original100%?now85%£340
the amount now, as a percentage of the original
85% = £340
divide to find 1%
1% =4
multiply by 100
100% =400
Original£400

After a 30% increase, a price is £91. Find the original price.

original100%?now130%£91
the amount now, as a percentage of the original
130% = £91
divide to find 1%
1% =0.7
multiply by 100
100% =70
Original£70

After a 35% decrease, a coat costs £52. Find the original price.

original100%?now65%£52
the amount now, as a percentage of the original
65% = £52
divide to find 1%
1% =0.8
multiply by 100
100% =80
Original£80

After a 30% increase, a price is £91. Find the original price.

original100%?now130%£91
the amount now, as a percentage of the original
130% = £91
divide to find 1%
1% =0.7
multiply by 100
100% =70
Original£70

A gym puts its monthly fee up by 12% to £28. Find the original fee.

original100%?now112%£28
the amount now, as a percentage of the original
112% = £28
divide to find 1%
1% =0.25
multiply by 100
100% =25
Original£25

After a 30% increase, a price is £91. Find the original price.

original100%?now130%£91
the amount now, as a percentage of the original
130% = £91
divide to find 1%
1% =0.7
multiply by 100
100% =70
Original£70

After a 5% increase, a train fare is £8.40. Find the original fare.

original100%?now105%£8.40
the amount now, as a percentage of the original
105% = £8.40
divide to find 1%
1% =0.08
multiply by 100
100% =8
Original£8

Reverse percentages worksheet, page 1

Answer sheet

  1. A price of £144 includes 20% VAT. How much of the £144 is VAT?

    £24

  2. A TV costs £360 after a 10% reduction. Mo says it was £396 before. Find his mistake and the real price.

    £400: £360 is 90%

A price goes up by 20%. Then the new price comes down by 20%. Is it back where it started?

No: it is 4% lower

  1. After a 25% increase, a price is £75. Find the original price.

    £60

  2. After a 20% decrease, a price is £56. Find the original price.

    £70

  3. After a 10% increase, a bag costs £66. Sam says it cost £59.40 before. What has he done wrong? Find the right price.

    £60 (£66 is 110%)
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