MathsAges 10-12

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.

New variation Try interactive challenge Browse templates

Age band:Ages 10-12 Ages 13-15

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 10-12

Reverse percentages: original value

Take your time. Show your thinking.

1. After a 10% increase, a quantity becomes 462. Find the original value before the change.
110% = 462 · 100% Original = ?
2. After a 40% decrease, a quantity becomes 204. Find the original value before the change.
60% = 204 · 100% Original = ?
3. After a 50% increase, a quantity becomes 900. Find the original value before the change.
150% = 900 · 100% Original = ?
4. After a 40% decrease, a quantity becomes 300. Find the original value before the change.
60% = 300 · 100% Original = ?
5. After a 10% increase, a quantity becomes 198. Find the original value before the change.
110% = 198 · 100% Original = ?
6. After a 40% decrease, a quantity becomes 48. Find the original value before the change.
60% = 48 · 100% Original = ?
7. After a 25% increase, a quantity becomes 375. Find the original value before the change.
125% = 375 · 100% Original = ?
8. After a 25% decrease, a quantity becomes 390. Find the original value before the change.
75% = 390 · 100% Original = ?
9. After a 20% decrease, a quantity becomes 320. Find the original value before the change.
80% = 320 · 100% Original = ?
10. After a 50% decrease, a quantity becomes 200. Find the original value before the change.
50% = 200 · 100% Original = ?
11. After a 50% decrease, a quantity becomes 30. Find the original value before the change.
50% = 30 · 100% Original = ?
12. After a 20% decrease, a quantity becomes 256. Find the original value before the change.
80% = 256 · 100% Original = ?

12 questions · Seed 51 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Reverse percentages: original value

Answers and reasoning. Review before teaching.

1. After a 10% increase, a quantity becomes 462. Find the original value before the change.
420
The new value is 110% of the original. Divide 462 by 1.1 to get 420.
2. After a 40% decrease, a quantity becomes 204. Find the original value before the change.
340
The new value is 60% of the original. Divide 204 by 0.6 to get 340.
3. 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.
4. After a 40% decrease, a quantity becomes 300. Find the original value before the change.
500
The new value is 60% of the original. Divide 300 by 0.6 to get 500.
5. After a 10% increase, a quantity becomes 198. Find the original value before the change.
180
The new value is 110% of the original. Divide 198 by 1.1 to get 180.
6. After a 40% decrease, a quantity becomes 48. Find the original value before the change.
80
The new value is 60% of the original. Divide 48 by 0.6 to get 80.
7. After a 25% increase, a quantity becomes 375. Find the original value before the change.
300
The new value is 125% of the original. Divide 375 by 1.25 to get 300.
8. After a 25% decrease, a quantity becomes 390. Find the original value before the change.
520
The new value is 75% of the original. Divide 390 by 0.75 to get 520.
9. After a 20% decrease, a quantity becomes 320. Find the original value before the change.
400
The new value is 80% of the original. Divide 320 by 0.8 to get 400.
10. After a 50% decrease, a quantity becomes 200. Find the original value before the change.
400
The new value is 50% of the original. Divide 200 by 0.5 to get 400.
11. After a 50% decrease, a quantity becomes 30. Find the original value before the change.
60
The new value is 50% of the original. Divide 30 by 0.5 to get 60.
12. After a 20% decrease, a quantity becomes 256. Find the original value before the change.
320
The new value is 80% of the original. Divide 256 by 0.8 to get 320.

12 questions · Seed 51 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Reverse percentages: original value

Take your time. Show your thinking.

1. After a 10% increase, a quantity becomes 462. Find the original value before the change.
110% = 462 · 100% Original = ?
2. After a 40% decrease, a quantity becomes 204. Find the original value before the change.
60% = 204 · 100% Original = ?
3. After a 50% increase, a quantity becomes 900. Find the original value before the change.
150% = 900 · 100% Original = ?
4. After a 40% decrease, a quantity becomes 300. Find the original value before the change.
60% = 300 · 100% Original = ?
5. After a 10% increase, a quantity becomes 198. Find the original value before the change.
110% = 198 · 100% Original = ?
6. After a 40% decrease, a quantity becomes 48. Find the original value before the change.
60% = 48 · 100% Original = ?
7. After a 25% increase, a quantity becomes 375. Find the original value before the change.
125% = 375 · 100% Original = ?
8. After a 25% decrease, a quantity becomes 390. Find the original value before the change.
75% = 390 · 100% Original = ?
9. After a 20% decrease, a quantity becomes 320. Find the original value before the change.
80% = 320 · 100% Original = ?
10. After a 50% decrease, a quantity becomes 200. Find the original value before the change.
50% = 200 · 100% Original = ?
11. After a 50% decrease, a quantity becomes 30. Find the original value before the change.
50% = 30 · 100% Original = ?
12. After a 20% decrease, a quantity becomes 256. Find the original value before the change.
80% = 256 · 100% Original = ?

12 questions · Seed 51 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Reverse percentages: original value

Answers and reasoning. Review before teaching.

1. After a 10% increase, a quantity becomes 462. Find the original value before the change.
420
The new value is 110% of the original. Divide 462 by 1.1 to get 420.
2. After a 40% decrease, a quantity becomes 204. Find the original value before the change.
340
The new value is 60% of the original. Divide 204 by 0.6 to get 340.
3. 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.
4. After a 40% decrease, a quantity becomes 300. Find the original value before the change.
500
The new value is 60% of the original. Divide 300 by 0.6 to get 500.
5. After a 10% increase, a quantity becomes 198. Find the original value before the change.
180
The new value is 110% of the original. Divide 198 by 1.1 to get 180.
6. After a 40% decrease, a quantity becomes 48. Find the original value before the change.
80
The new value is 60% of the original. Divide 48 by 0.6 to get 80.
7. After a 25% increase, a quantity becomes 375. Find the original value before the change.
300
The new value is 125% of the original. Divide 375 by 1.25 to get 300.
8. After a 25% decrease, a quantity becomes 390. Find the original value before the change.
520
The new value is 75% of the original. Divide 390 by 0.75 to get 520.
9. After a 20% decrease, a quantity becomes 320. Find the original value before the change.
400
The new value is 80% of the original. Divide 320 by 0.8 to get 400.
10. After a 50% decrease, a quantity becomes 200. Find the original value before the change.
400
The new value is 50% of the original. Divide 200 by 0.5 to get 400.
11. After a 50% decrease, a quantity becomes 30. Find the original value before the change.
60
The new value is 50% of the original. Divide 30 by 0.5 to get 60.
12. After a 20% decrease, a quantity becomes 256. Find the original value before the change.
320
The new value is 80% of the original. Divide 256 by 0.8 to get 320.

12 questions · Seed 51 · Age guidance, not curriculum certification