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 30% increase, a quantity becomes 208. Find the original value before the change.
130% = 208 · 100% Original = ?
2. After a 10% decrease, a quantity becomes 144. Find the original value before the change.
90% = 144 · 100% Original = ?
3. After a 50% decrease, a quantity becomes 170. Find the original value before the change.
50% = 170 · 100% Original = ?
4. After a 15% increase, a quantity becomes 460. Find the original value before the change.
115% = 460 · 100% Original = ?
5. After a 30% decrease, a quantity becomes 336. Find the original value before the change.
70% = 336 · 100% Original = ?
6. After a 40% decrease, a quantity becomes 120. Find the original value before the change.
60% = 120 · 100% Original = ?
7. After a 30% increase, a quantity becomes 260. Find the original value before the change.
130% = 260 · 100% Original = ?
8. After a 15% increase, a quantity becomes 506. Find the original value before the change.
115% = 506 · 100% Original = ?
9. After a 10% decrease, a quantity becomes 540. Find the original value before the change.
90% = 540 · 100% Original = ?
10. After a 30% decrease, a quantity becomes 126. Find the original value before the change.
70% = 126 · 100% Original = ?
11. After a 25% decrease, a quantity becomes 30. Find the original value before the change.
75% = 30 · 100% Original = ?
12. After a 50% decrease, a quantity becomes 280. Find the original value before the change.
50% = 280 · 100% Original = ?

12 questions · Seed 49 · 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 30% increase, a quantity becomes 208. Find the original value before the change.
160
The new value is 130% of the original. Divide 208 by 1.3 to get 160.
2. After a 10% decrease, a quantity becomes 144. Find the original value before the change.
160
The new value is 90% of the original. Divide 144 by 0.9 to get 160.
3. After a 50% decrease, a quantity becomes 170. Find the original value before the change.
340
The new value is 50% of the original. Divide 170 by 0.5 to get 340.
4. After a 15% increase, a quantity becomes 460. Find the original value before the change.
400
The new value is 115% of the original. Divide 460 by 1.15 to get 400.
5. After a 30% decrease, a quantity becomes 336. Find the original value before the change.
480
The new value is 70% of the original. Divide 336 by 0.7 to get 480.
6. After a 40% decrease, a quantity becomes 120. Find the original value before the change.
200
The new value is 60% of the original. Divide 120 by 0.6 to get 200.
7. After a 30% increase, a quantity becomes 260. Find the original value before the change.
200
The new value is 130% of the original. Divide 260 by 1.3 to get 200.
8. After a 15% increase, a quantity becomes 506. Find the original value before the change.
440
The new value is 115% of the original. Divide 506 by 1.15 to get 440.
9. After a 10% decrease, a quantity becomes 540. Find the original value before the change.
600
The new value is 90% of the original. Divide 540 by 0.9 to get 600.
10. After a 30% decrease, a quantity becomes 126. Find the original value before the change.
180
The new value is 70% of the original. Divide 126 by 0.7 to get 180.
11. After a 25% decrease, a quantity becomes 30. Find the original value before the change.
40
The new value is 75% of the original. Divide 30 by 0.75 to get 40.
12. 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.

12 questions · Seed 49 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Reverse percentages: original value

Take your time. Show your thinking.

1. After a 30% increase, a quantity becomes 208. Find the original value before the change.
130% = 208 · 100% Original = ?
2. After a 10% decrease, a quantity becomes 144. Find the original value before the change.
90% = 144 · 100% Original = ?
3. After a 50% decrease, a quantity becomes 170. Find the original value before the change.
50% = 170 · 100% Original = ?
4. After a 15% increase, a quantity becomes 460. Find the original value before the change.
115% = 460 · 100% Original = ?
5. After a 30% decrease, a quantity becomes 336. Find the original value before the change.
70% = 336 · 100% Original = ?
6. After a 40% decrease, a quantity becomes 120. Find the original value before the change.
60% = 120 · 100% Original = ?
7. After a 30% increase, a quantity becomes 260. Find the original value before the change.
130% = 260 · 100% Original = ?
8. After a 15% increase, a quantity becomes 506. Find the original value before the change.
115% = 506 · 100% Original = ?
9. After a 10% decrease, a quantity becomes 540. Find the original value before the change.
90% = 540 · 100% Original = ?
10. After a 30% decrease, a quantity becomes 126. Find the original value before the change.
70% = 126 · 100% Original = ?
11. After a 25% decrease, a quantity becomes 30. Find the original value before the change.
75% = 30 · 100% Original = ?
12. After a 50% decrease, a quantity becomes 280. Find the original value before the change.
50% = 280 · 100% Original = ?

12 questions · Seed 49 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Reverse percentages: original value

Answers and reasoning. Review before teaching.

1. After a 30% increase, a quantity becomes 208. Find the original value before the change.
160
The new value is 130% of the original. Divide 208 by 1.3 to get 160.
2. After a 10% decrease, a quantity becomes 144. Find the original value before the change.
160
The new value is 90% of the original. Divide 144 by 0.9 to get 160.
3. After a 50% decrease, a quantity becomes 170. Find the original value before the change.
340
The new value is 50% of the original. Divide 170 by 0.5 to get 340.
4. After a 15% increase, a quantity becomes 460. Find the original value before the change.
400
The new value is 115% of the original. Divide 460 by 1.15 to get 400.
5. After a 30% decrease, a quantity becomes 336. Find the original value before the change.
480
The new value is 70% of the original. Divide 336 by 0.7 to get 480.
6. After a 40% decrease, a quantity becomes 120. Find the original value before the change.
200
The new value is 60% of the original. Divide 120 by 0.6 to get 200.
7. After a 30% increase, a quantity becomes 260. Find the original value before the change.
200
The new value is 130% of the original. Divide 260 by 1.3 to get 200.
8. After a 15% increase, a quantity becomes 506. Find the original value before the change.
440
The new value is 115% of the original. Divide 506 by 1.15 to get 440.
9. After a 10% decrease, a quantity becomes 540. Find the original value before the change.
600
The new value is 90% of the original. Divide 540 by 0.9 to get 600.
10. After a 30% decrease, a quantity becomes 126. Find the original value before the change.
180
The new value is 70% of the original. Divide 126 by 0.7 to get 180.
11. After a 25% decrease, a quantity becomes 30. Find the original value before the change.
40
The new value is 75% of the original. Divide 30 by 0.75 to get 40.
12. 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.

12 questions · Seed 49 · Age guidance, not curriculum certification