1. Reverse Percentages – Calculator – Demonstration
This resource provides animated demonstrations of the mathematical method.
Check animations and delete slides not needed for your class.

2. 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?
× 1.2
100%
120% ?
$300
$360
÷ 1.2

3. I invested some money in the bank and got 40% interest.
At the end of the year I had $630.
How much did I put in the bank?
× 1.4
100%
140% ?
$450
$630
÷ 1.4

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?
× 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?
× 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?
× 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?
× 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?
× 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?
$135.34

9. A pair of jeans were 30% off and cost $42.
How much were they before the sale?
× 0.7
100%
70% ?
$60
$42
SALE!
÷ 0.7

10. A pair of jeans were 40% off and cost $54.
How much were they before the sale?
× 0.6
100%
60% ?
$90
$54
SALE!
÷ 0.6

11. A pair of shoes were 24% off and cost $38.
How much were they before the sale?
× 0.76
100%
76% ?
$50
$38
SALE!
÷ 0.76

12. A pair of shoes were 8% off and cost $74.
How much were they before the sale?
× 0.92
100%
92%
$80.43 ?
$74
SALE!
÷ 0.92

13. A pair of shoes were 7.8% off and cost $64.
How much were they before the sale?
× 0.922
100%
92.2%
$69.41 ?
$64
SALE!
÷ 0.922

14. Answers 40% off! Now $36! 24% off! Now $26! 9% off! Now $43!
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?
× 0.7
100%
70% ?
$78
24% off!
Now $26!
÷ 0.7
9% off!
Now $43!
Answers
7.25% off!
Now $73!

15. Answers 40% off! Now $36! Were $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?
Were $60
× 0.7
100%
70% ?
$78
24% off!
Now $26!
÷ 0.7
Was $34.21
9% off!
Now $43!
Answers
7.25% off!
Now $73!
Were $47.25
Was $78.71

16. 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?
× 1.2
× 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 = ?

17. 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?
× 1.2
× 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

18. 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 of 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?

19. 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 of 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

21. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
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