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 50% decrease, a quantity becomes 280. Find the original value before the change.
50% = 280 · 100% Original = ?
2. After a 50% increase, a quantity becomes 240. Find the original value before the change.
150% = 240 · 100% Original = ?
3. After a 20% decrease, a quantity becomes 336. Find the original value before the change.
80% = 336 · 100% Original = ?
4. After a 30% decrease, a quantity becomes 196. Find the original value before the change.
70% = 196 · 100% Original = ?
5. After a 20% increase, a quantity becomes 48. Find the original value before the change.
120% = 48 · 100% Original = ?
6. After a 20% decrease, a quantity becomes 176. Find the original value before the change.
80% = 176 · 100% Original = ?
7. After a 10% decrease, a quantity becomes 450. Find the original value before the change.
90% = 450 · 100% Original = ?
8. After a 30% increase, a quantity becomes 390. Find the original value before the change.
130% = 390 · 100% Original = ?
9. After a 50% decrease, a quantity becomes 250. Find the original value before the change.
50% = 250 · 100% Original = ?
10. After a 50% increase, a quantity becomes 900. Find the original value before the change.
150% = 900 · 100% Original = ?
11. After a 10% decrease, a quantity becomes 72. Find the original value before the change.
90% = 72 · 100% Original = ?
12. After a 15% decrease, a quantity becomes 204. Find the original value before the change.
85% = 204 · 100% Original = ?

12 questions · Seed 43 · 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 50% decrease, a quantity becomes 280. Find the original value before the change.
560
The new value is 50% of the original. Divide 280 by 0.5 to get 560.
2. After a 50% increase, a quantity becomes 240. Find the original value before the change.
160
The new value is 150% of the original. Divide 240 by 1.5 to get 160.
3. After a 20% decrease, a quantity becomes 336. Find the original value before the change.
420
The new value is 80% of the original. Divide 336 by 0.8 to get 420.
4. After a 30% decrease, a quantity becomes 196. Find the original value before the change.
280
The new value is 70% of the original. Divide 196 by 0.7 to get 280.
5. After a 20% increase, a quantity becomes 48. Find the original value before the change.
40
The new value is 120% of the original. Divide 48 by 1.2 to get 40.
6. After a 20% decrease, a quantity becomes 176. Find the original value before the change.
220
The new value is 80% of the original. Divide 176 by 0.8 to get 220.
7. After a 10% decrease, a quantity becomes 450. Find the original value before the change.
500
The new value is 90% of the original. Divide 450 by 0.9 to get 500.
8. After a 30% increase, a quantity becomes 390. Find the original value before the change.
300
The new value is 130% of the original. Divide 390 by 1.3 to get 300.
9. After a 50% decrease, a quantity becomes 250. Find the original value before the change.
500
The new value is 50% of the original. Divide 250 by 0.5 to get 500.
10. After a 50% increase, a quantity becomes 900. Find the original value before the change.
600
The new value is 150% of the original. Divide 900 by 1.5 to get 600.
11. After a 10% decrease, a quantity becomes 72. Find the original value before the change.
80
The new value is 90% of the original. Divide 72 by 0.9 to get 80.
12. After a 15% decrease, a quantity becomes 204. Find the original value before the change.
240
The new value is 85% of the original. Divide 204 by 0.85 to get 240.

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Reverse percentages: original value

Take your time. Show your thinking.

1. After a 50% decrease, a quantity becomes 280. Find the original value before the change.
50% = 280 · 100% Original = ?
2. After a 50% increase, a quantity becomes 240. Find the original value before the change.
150% = 240 · 100% Original = ?
3. After a 20% decrease, a quantity becomes 336. Find the original value before the change.
80% = 336 · 100% Original = ?
4. After a 30% decrease, a quantity becomes 196. Find the original value before the change.
70% = 196 · 100% Original = ?
5. After a 20% increase, a quantity becomes 48. Find the original value before the change.
120% = 48 · 100% Original = ?
6. After a 20% decrease, a quantity becomes 176. Find the original value before the change.
80% = 176 · 100% Original = ?
7. After a 10% decrease, a quantity becomes 450. Find the original value before the change.
90% = 450 · 100% Original = ?
8. After a 30% increase, a quantity becomes 390. Find the original value before the change.
130% = 390 · 100% Original = ?
9. After a 50% decrease, a quantity becomes 250. Find the original value before the change.
50% = 250 · 100% Original = ?
10. After a 50% increase, a quantity becomes 900. Find the original value before the change.
150% = 900 · 100% Original = ?
11. After a 10% decrease, a quantity becomes 72. Find the original value before the change.
90% = 72 · 100% Original = ?
12. After a 15% decrease, a quantity becomes 204. Find the original value before the change.
85% = 204 · 100% Original = ?

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Reverse percentages: original value

Answers and reasoning. Review before teaching.

1. After a 50% decrease, a quantity becomes 280. Find the original value before the change.
560
The new value is 50% of the original. Divide 280 by 0.5 to get 560.
2. After a 50% increase, a quantity becomes 240. Find the original value before the change.
160
The new value is 150% of the original. Divide 240 by 1.5 to get 160.
3. After a 20% decrease, a quantity becomes 336. Find the original value before the change.
420
The new value is 80% of the original. Divide 336 by 0.8 to get 420.
4. After a 30% decrease, a quantity becomes 196. Find the original value before the change.
280
The new value is 70% of the original. Divide 196 by 0.7 to get 280.
5. After a 20% increase, a quantity becomes 48. Find the original value before the change.
40
The new value is 120% of the original. Divide 48 by 1.2 to get 40.
6. After a 20% decrease, a quantity becomes 176. Find the original value before the change.
220
The new value is 80% of the original. Divide 176 by 0.8 to get 220.
7. After a 10% decrease, a quantity becomes 450. Find the original value before the change.
500
The new value is 90% of the original. Divide 450 by 0.9 to get 500.
8. After a 30% increase, a quantity becomes 390. Find the original value before the change.
300
The new value is 130% of the original. Divide 390 by 1.3 to get 300.
9. After a 50% decrease, a quantity becomes 250. Find the original value before the change.
500
The new value is 50% of the original. Divide 250 by 0.5 to get 500.
10. After a 50% increase, a quantity becomes 900. Find the original value before the change.
600
The new value is 150% of the original. Divide 900 by 1.5 to get 600.
11. After a 10% decrease, a quantity becomes 72. Find the original value before the change.
80
The new value is 90% of the original. Divide 72 by 0.9 to get 80.
12. After a 15% decrease, a quantity becomes 204. Find the original value before the change.
240
The new value is 85% of the original. Divide 204 by 0.85 to get 240.

12 questions · Seed 43 · Age guidance, not curriculum certification