MathsAges 13-15

Reverse percentages: original value

Work backwards from a percentage-increased or percentage-decreased value to find the original 100% quantity. Review suitability for your learners before teaching.

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Age band:Ages 10-12 Ages 13-15

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Worksheet StudioPractice pack · Ages 13-15

Reverse percentages: original value

Take your time. Show your thinking.

1. After a 10% increase, a quantity becomes 220. Find the original value before the change.
110% = 220 · 100% Original = ?
2. After a 20% increase, a quantity becomes 672. Find the original value before the change.
120% = 672 · 100% Original = ?
3. After a 10% decrease, a quantity becomes 288. Find the original value before the change.
90% = 288 · 100% Original = ?
4. After a 15% decrease, a quantity becomes 510. Find the original value before the change.
85% = 510 · 100% Original = ?
5. After a 30% increase, a quantity becomes 156. Find the original value before the change.
130% = 156 · 100% Original = ?
6. After a 10% decrease, a quantity becomes 216. Find the original value before the change.
90% = 216 · 100% Original = ?
7. After a 40% increase, a quantity becomes 280. Find the original value before the change.
140% = 280 · 100% Original = ?
8. After a 20% increase, a quantity becomes 720. Find the original value before the change.
120% = 720 · 100% Original = ?
9. After a 10% decrease, a quantity becomes 324. Find the original value before the change.
90% = 324 · 100% Original = ?
10. After a 15% increase, a quantity becomes 253. Find the original value before the change.
115% = 253 · 100% Original = ?
11. After a 30% decrease, a quantity becomes 42. Find the original value before the change.
70% = 42 · 100% Original = ?
12. After a 20% increase, a quantity becomes 96. Find the original value before the change.
120% = 96 · 100% Original = ?

12 questions · Seed 44 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Reverse percentages: original value

Answers and reasoning. Review before teaching.

1. After a 10% increase, a quantity becomes 220. Find the original value before the change.
200
The new value is 110% of the original. Divide 220 by 1.1 to get 200.
2. After a 20% increase, a quantity becomes 672. Find the original value before the change.
560
The new value is 120% of the original. Divide 672 by 1.2 to get 560.
3. After a 10% decrease, a quantity becomes 288. Find the original value before the change.
320
The new value is 90% of the original. Divide 288 by 0.9 to get 320.
4. After a 15% decrease, a quantity becomes 510. Find the original value before the change.
600
The new value is 85% of the original. Divide 510 by 0.85 to get 600.
5. After a 30% increase, a quantity becomes 156. Find the original value before the change.
120
The new value is 130% of the original. Divide 156 by 1.3 to get 120.
6. After a 10% decrease, a quantity becomes 216. Find the original value before the change.
240
The new value is 90% of the original. Divide 216 by 0.9 to get 240.
7. After a 40% increase, a quantity becomes 280. Find the original value before the change.
200
The new value is 140% of the original. Divide 280 by 1.4 to get 200.
8. After a 20% increase, a quantity becomes 720. Find the original value before the change.
600
The new value is 120% of the original. Divide 720 by 1.2 to get 600.
9. After a 10% decrease, a quantity becomes 324. Find the original value before the change.
360
The new value is 90% of the original. Divide 324 by 0.9 to get 360.
10. After a 15% increase, a quantity becomes 253. Find the original value before the change.
220
The new value is 115% of the original. Divide 253 by 1.15 to get 220.
11. After a 30% decrease, a quantity becomes 42. Find the original value before the change.
60
The new value is 70% of the original. Divide 42 by 0.7 to get 60.
12. After a 20% increase, a quantity becomes 96. Find the original value before the change.
80
The new value is 120% of the original. Divide 96 by 1.2 to get 80.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Reverse percentages: original value

Take your time. Show your thinking.

1. After a 10% increase, a quantity becomes 220. Find the original value before the change.
110% = 220 · 100% Original = ?
2. After a 20% increase, a quantity becomes 672. Find the original value before the change.
120% = 672 · 100% Original = ?
3. After a 10% decrease, a quantity becomes 288. Find the original value before the change.
90% = 288 · 100% Original = ?
4. After a 15% decrease, a quantity becomes 510. Find the original value before the change.
85% = 510 · 100% Original = ?
5. After a 30% increase, a quantity becomes 156. Find the original value before the change.
130% = 156 · 100% Original = ?
6. After a 10% decrease, a quantity becomes 216. Find the original value before the change.
90% = 216 · 100% Original = ?
7. After a 40% increase, a quantity becomes 280. Find the original value before the change.
140% = 280 · 100% Original = ?
8. After a 20% increase, a quantity becomes 720. Find the original value before the change.
120% = 720 · 100% Original = ?
9. After a 10% decrease, a quantity becomes 324. Find the original value before the change.
90% = 324 · 100% Original = ?
10. After a 15% increase, a quantity becomes 253. Find the original value before the change.
115% = 253 · 100% Original = ?
11. After a 30% decrease, a quantity becomes 42. Find the original value before the change.
70% = 42 · 100% Original = ?
12. After a 20% increase, a quantity becomes 96. Find the original value before the change.
120% = 96 · 100% Original = ?

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Reverse percentages: original value

Answers and reasoning. Review before teaching.

1. After a 10% increase, a quantity becomes 220. Find the original value before the change.
200
The new value is 110% of the original. Divide 220 by 1.1 to get 200.
2. After a 20% increase, a quantity becomes 672. Find the original value before the change.
560
The new value is 120% of the original. Divide 672 by 1.2 to get 560.
3. After a 10% decrease, a quantity becomes 288. Find the original value before the change.
320
The new value is 90% of the original. Divide 288 by 0.9 to get 320.
4. After a 15% decrease, a quantity becomes 510. Find the original value before the change.
600
The new value is 85% of the original. Divide 510 by 0.85 to get 600.
5. After a 30% increase, a quantity becomes 156. Find the original value before the change.
120
The new value is 130% of the original. Divide 156 by 1.3 to get 120.
6. After a 10% decrease, a quantity becomes 216. Find the original value before the change.
240
The new value is 90% of the original. Divide 216 by 0.9 to get 240.
7. After a 40% increase, a quantity becomes 280. Find the original value before the change.
200
The new value is 140% of the original. Divide 280 by 1.4 to get 200.
8. After a 20% increase, a quantity becomes 720. Find the original value before the change.
600
The new value is 120% of the original. Divide 720 by 1.2 to get 600.
9. After a 10% decrease, a quantity becomes 324. Find the original value before the change.
360
The new value is 90% of the original. Divide 324 by 0.9 to get 360.
10. After a 15% increase, a quantity becomes 253. Find the original value before the change.
220
The new value is 115% of the original. Divide 253 by 1.15 to get 220.
11. After a 30% decrease, a quantity becomes 42. Find the original value before the change.
60
The new value is 70% of the original. Divide 42 by 0.7 to get 60.
12. After a 20% increase, a quantity becomes 96. Find the original value before the change.
80
The new value is 120% of the original. Divide 96 by 1.2 to get 80.

12 questions · Seed 44 · Age guidance, not curriculum certification