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.

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Age band:Ages 10-12 Ages 13-15

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Worksheet StudioPractice pack · Ages 10-12

Reverse percentages: original value

Take your time. Show your thinking.

1. After a 10% increase, a quantity becomes 286. Find the original value before the change.
110% = 286 · 100% Original = ?
2. After a 15% decrease, a quantity becomes 102. Find the original value before the change.
85% = 102 · 100% Original = ?
3. After a 15% decrease, a quantity becomes 357. Find the original value before the change.
85% = 357 · 100% Original = ?
4. After a 15% increase, a quantity becomes 552. Find the original value before the change.
115% = 552 · 100% Original = ?
5. After a 30% increase, a quantity becomes 780. Find the original value before the change.
130% = 780 · 100% Original = ?
6. After a 20% decrease, a quantity becomes 144. Find the original value before the change.
80% = 144 · 100% Original = ?
7. After a 50% decrease, a quantity becomes 160. Find the original value before the change.
50% = 160 · 100% Original = ?
8. After a 50% increase, a quantity becomes 150. Find the original value before the change.
150% = 150 · 100% Original = ?
9. After a 15% increase, a quantity becomes 138. Find the original value before the change.
115% = 138 · 100% Original = ?
10. After a 15% decrease, a quantity becomes 238. Find the original value before the change.
85% = 238 · 100% Original = ?
11. After a 20% decrease, a quantity becomes 192. Find the original value before the change.
80% = 192 · 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 46 · 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 286. Find the original value before the change.
260
The new value is 110% of the original. Divide 286 by 1.1 to get 260.
2. After a 15% decrease, a quantity becomes 102. Find the original value before the change.
120
The new value is 85% of the original. Divide 102 by 0.85 to get 120.
3. After a 15% decrease, a quantity becomes 357. Find the original value before the change.
420
The new value is 85% of the original. Divide 357 by 0.85 to get 420.
4. After a 15% increase, a quantity becomes 552. Find the original value before the change.
480
The new value is 115% of the original. Divide 552 by 1.15 to get 480.
5. After a 30% increase, a quantity becomes 780. Find the original value before the change.
600
The new value is 130% of the original. Divide 780 by 1.3 to get 600.
6. After a 20% decrease, a quantity becomes 144. Find the original value before the change.
180
The new value is 80% of the original. Divide 144 by 0.8 to get 180.
7. After a 50% decrease, a quantity becomes 160. Find the original value before the change.
320
The new value is 50% of the original. Divide 160 by 0.5 to get 320.
8. After a 50% increase, a quantity becomes 150. Find the original value before the change.
100
The new value is 150% of the original. Divide 150 by 1.5 to get 100.
9. After a 15% increase, a quantity becomes 138. Find the original value before the change.
120
The new value is 115% of the original. Divide 138 by 1.15 to get 120.
10. After a 15% decrease, a quantity becomes 238. Find the original value before the change.
280
The new value is 85% of the original. Divide 238 by 0.85 to get 280.
11. After a 20% decrease, a quantity becomes 192. Find the original value before the change.
240
The new value is 80% of the original. Divide 192 by 0.8 to get 240.
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 46 · 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 286. Find the original value before the change.
110% = 286 · 100% Original = ?
2. After a 15% decrease, a quantity becomes 102. Find the original value before the change.
85% = 102 · 100% Original = ?
3. After a 15% decrease, a quantity becomes 357. Find the original value before the change.
85% = 357 · 100% Original = ?
4. After a 15% increase, a quantity becomes 552. Find the original value before the change.
115% = 552 · 100% Original = ?
5. After a 30% increase, a quantity becomes 780. Find the original value before the change.
130% = 780 · 100% Original = ?
6. After a 20% decrease, a quantity becomes 144. Find the original value before the change.
80% = 144 · 100% Original = ?
7. After a 50% decrease, a quantity becomes 160. Find the original value before the change.
50% = 160 · 100% Original = ?
8. After a 50% increase, a quantity becomes 150. Find the original value before the change.
150% = 150 · 100% Original = ?
9. After a 15% increase, a quantity becomes 138. Find the original value before the change.
115% = 138 · 100% Original = ?
10. After a 15% decrease, a quantity becomes 238. Find the original value before the change.
85% = 238 · 100% Original = ?
11. After a 20% decrease, a quantity becomes 192. Find the original value before the change.
80% = 192 · 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 46 · 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 286. Find the original value before the change.
260
The new value is 110% of the original. Divide 286 by 1.1 to get 260.
2. After a 15% decrease, a quantity becomes 102. Find the original value before the change.
120
The new value is 85% of the original. Divide 102 by 0.85 to get 120.
3. After a 15% decrease, a quantity becomes 357. Find the original value before the change.
420
The new value is 85% of the original. Divide 357 by 0.85 to get 420.
4. After a 15% increase, a quantity becomes 552. Find the original value before the change.
480
The new value is 115% of the original. Divide 552 by 1.15 to get 480.
5. After a 30% increase, a quantity becomes 780. Find the original value before the change.
600
The new value is 130% of the original. Divide 780 by 1.3 to get 600.
6. After a 20% decrease, a quantity becomes 144. Find the original value before the change.
180
The new value is 80% of the original. Divide 144 by 0.8 to get 180.
7. After a 50% decrease, a quantity becomes 160. Find the original value before the change.
320
The new value is 50% of the original. Divide 160 by 0.5 to get 320.
8. After a 50% increase, a quantity becomes 150. Find the original value before the change.
100
The new value is 150% of the original. Divide 150 by 1.5 to get 100.
9. After a 15% increase, a quantity becomes 138. Find the original value before the change.
120
The new value is 115% of the original. Divide 138 by 1.15 to get 120.
10. After a 15% decrease, a quantity becomes 238. Find the original value before the change.
280
The new value is 85% of the original. Divide 238 by 0.85 to get 280.
11. After a 20% decrease, a quantity becomes 192. Find the original value before the change.
240
The new value is 80% of the original. Divide 192 by 0.8 to get 240.
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 46 · Age guidance, not curriculum certification