1. goteachmaths.co.uk Reverse Percentages – Complete Lesson
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2. (Finding an original amount)
13 November November 2018
Reverse Percentage
(Finding an original amount)

3. I invested some money in the bank and got 20% interest.
At the end of the year I had $360.
How much did I put in the bank?
x 1.2
100%
120% ?
$300
$360
÷ 1.2

4. I invested some money in the bank and got 45% interest.
At the end of the year I had $
How much did I put in the bank?
x 1.45
100%
145% ?
$450
$652.50
÷ 1.45

5. This year oil increased by 15% to $109.25 per barrel.
How much did a barrel cost at the start of the year?
x 1.15
100%
115% ?
$95
$109.25
÷ 1.15

6. This year oil increased by 7.5% to $97 per barrel.
How much did a barrel cost at the start of the year?
x 1.075
100%
107.5%
$90.23 ?
$97
2 d.p. Why?
÷ 1.075

7. Oil was $65 after a 40% increase. What was its original price?
Example:
Oil went up 20% and cost $48.
How much was it before the increase?
A T-shirt was $28 after a 15% tax.
What was its original price?
x 1.2
100%
120% ?
$48
A dress was $65 after a 12.5% increase.
What was its original price?
÷ 1.2
Petrol increased to $ after
a 7.4% tax. What was its original price?

8. Answers Oil was $65 after a 40% increase. What was its original price?
Example:
$46.43
Oil went up 20% and cost $48.
How much was it before the increase?
A T-shirt was $28 after a 15% tax.
What was its original price?
x 1.2
$24.35
100%
120% ?
$48
A dress was $65 after a 12.5% increase.
What was its original price?
÷ 1.2
$57.78
Answers
Petrol increased to $ after
a 7.4% tax. What was its original price?
$135.33

9. A pair of shoes increased
in value by 30%.
They are now $260.
How much were they before
the price increase?
A car increased
in value by 25%.
It is now $30,000.
How much was it before
the price increase?
A litre of oil increased
in value by 14.7%.
It is now $285.
How much was it before
the price increase?
A house increased
in value by 3.5%.
It is now $365,000.
How much was it before
the price increase?

10. Answers $200 $24,000 $248.47 $352,657.00 A pair of shoes increased
in value by 30%.
They are now $260.
How much were they before
the price increase?
A car increased
in value by 25%.
It is now $30,000.
How much was it before
the price increase?
$200
$24,000
A litre of oil increased
in value by 14.7%.
It is now $285.
How much was it before
the price increase?
A house increased
in value by 3.5%.
It is now $365,000.
How much was it before
the price increase?
$248.47
$352,657.00

11. A pair of shoes increased
in value by 40%.
They are now $420.
How much were they before
the price increase?
A car increased
in value by 17%.
It is now $37,440.
How much was it before
the price increase?
A litre of oil increased
in value by 5.9%.
It is now $178.
How much was it before
the price increase?
A house increased
in value by 1.345%.
It is now $435,505.
How much was it before
the price increase?

12. Answers $300 $32,000 $168.08 $429,725.20 A pair of shoes increased
in value by 40%.
They are now $420.
How much were they before
the price increase?
A car increased
in value by 17%.
It is now $37,440.
How much was it before
the price increase?
$300
$32,000
A litre of oil increased
in value by 5.9%.
It is now $178.
How much was it before
the price increase?
A house increased
in value by 1.345%.
It is now $435,505.
How much was it before
the price increase?
$168.08
$429,725.20

13. A pair of jeans was 30% off and cost $42.
How much was it before the sale?
x 0.7
100%
70% ?
$60
$42
SALE!
÷ 0.7

14. A pair of jeans was 60% off and cost $54.
How much was it before the sale?
x 0.6
100%
60% ?
$90
$54
SALE!
÷ 0.6

15. A pair of shoes was 24% off and cost $38.
How much was it before the sale?
x 0.76
100%
76% ?
$50
$38
SALE!
÷ 0.76

16. A pair of shoes was 7.8% off and cost $64.
How much was it before the sale?
x 0.922
100%
76%
$69.41 ?
$64
SALE!
÷ 0.922

17. 40% off! Now $36! 24% off! Now $26! 12.5% off! Now $43! 7.25% off!
Find the original prices
for these goods.
40% off!
Now $36!
Example:
A pair of shoes were $78 in the 30% off sale.
How much were they before the decrease?
x 0.7
100%
70% ?
$78
24% off!
Now $26!
÷ 0.7
12.5% off!
Now $43!
7.25% off!
Now $73!

18. Answers 40% off! Now $36! Was $60 24% off! Now $26! Was $34.21
Find the original prices
for these goods.
40% off!
Now $36!
Example:
A pair of shoes were $78 in the 30% off sale.
How much were they before the decrease?
Was $60
x 0.7
100%
70% ?
$78
24% off!
Now $26!
÷ 0.7
Was $34.21
12.5% off!
Now $43!
Answers
7.25% off!
Now $73!
Was $49.14
Was $78.71

19. Oil was $65 after a 30% increase. Original price = ?
Oil went up 20% and cost $48.
How much was it before the increase?
A T-shirt was 60% off and cost $54.
How much was it before the sale?
x 1.2
x 0.4
100%
120%
100%
40% ?
$48 ?
$54
÷ 1.2
÷ 0.4
Oil was $65 after a 30% increase.
Original price = ?
A T-shirt was $42 with 30% off.
Original price = ?
Oil was $78 after a 44% increase.
Original price = ?
A T-shirt was $43 with 24% off.
Original price = ?
Oil was $92 after a 7% increase.
Original price = ?
A T-shirt was $35 with 8% off.
Original price = ?

20. Answers Oil was $65 after a 30% increase. Original price = $50
Oil went up 20% and cost $48.
How much was it before the increase?
A T-shirt was 60% off and cost $54.
How much was it before the sale?
x 1.2
x 0.4
100%
120%
100%
40% ?
$48 ?
$54
÷ 1.2
÷ 0.4
Answers
Oil was $65 after a 30% increase.
Original price = $50
A T-shirt was $42 with 30% off.
Original price = $60
Oil was $78 after a 44% increase.
Original price = $54.17
A T-shirt was $43 with 24% off.
Original price = $56.58
Oil was $92 after a 7% increase.
Original price = $85.98
A T-shirt was $35 with 8% off.
Original price = $38.04

21. Discount = Price decrease
Tax = Price increase
Discount = Price decrease

23. ¼ PAGE 1) A T-shirt is sold with a 20% discount. It is sold for $67.
What was its original price?
2) There is 24% off a pair in shoes in the shop. It now costs
$65. What was its original price?
3) After a tax of 22%, a car sells for $9800.
What was its original price?
A shop sells milk for $2.50 a litre. This includes a tax of 27%.
How much is a litre of milk without tax?
A gallon of oil is taxed 18% by the government. One garage gives
a 25% discount and sells a gallon for $4.67.
What was its original price?

24. ¼ PAGE
Answers
1) A T-shirt is sold with a 20% discount. It is sold for $67.
What was its original price?
$83.75
2) There is 24% off a pair in shoes in the shop. It now costs
$65. What was its original price?
$85.53
3) After a tax of 22%, a car sells for $9800.
What was its original price? $
A shop sells milk for $2.50 a litre. This includes a tax of 27%.
How much is a litre of milk without tax?
$1.97
A gallon of oil is taxed 18% by the government. One garage gives
a 25% discount and sells a gallon for $4.67.
What was its original price?
$5.28

25. Check your success! I can calculate the original quantity
following an increase.
I can calculate the original quantity
following a decrease.
I am confident calculating reverse percentages.

26. Check your success! I can calculate the original quantity
following an increase.
I can calculate the original quantity
following a decrease.
I am confident calculating reverse percentages.

27. Write a text message to a friend describing:
How calculate a ‘reverse percentage’.

28. At auction Julia bought an antique chair,
then sold it for $54.
She made a 25% profit.
How much did the chair
originally cost Julia?