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 15% increase, a quantity becomes 69. Find the original value before the change.
115% = 69 · 100% Original = ?
2. After a 20% decrease, a quantity becomes 128. Find the original value before the change.
80% = 128 · 100% Original = ?
3. After a 50% increase, a quantity becomes 120. Find the original value before the change.
150% = 120 · 100% Original = ?
4. After a 30% increase, a quantity becomes 338. Find the original value before the change.
130% = 338 · 100% Original = ?
5. After a 20% increase, a quantity becomes 216. Find the original value before the change.
120% = 216 · 100% Original = ?
6. After a 10% decrease, a quantity becomes 270. Find the original value before the change.
90% = 270 · 100% Original = ?
7. After a 40% decrease, a quantity becomes 192. Find the original value before the change.
60% = 192 · 100% Original = ?
8. After a 40% decrease, a quantity becomes 252. Find the original value before the change.
60% = 252 · 100% Original = ?
9. After a 20% increase, a quantity becomes 168. Find the original value before the change.
120% = 168 · 100% Original = ?
10. After a 25% decrease, a quantity becomes 90. Find the original value before the change.
75% = 90 · 100% Original = ?
11. After a 30% decrease, a quantity becomes 168. Find the original value before the change.
70% = 168 · 100% Original = ?
12. After a 25% decrease, a quantity becomes 240. Find the original value before the change.
75% = 240 · 100% Original = ?

12 questions · Seed 45 · 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 15% increase, a quantity becomes 69. Find the original value before the change.
60
The new value is 115% of the original. Divide 69 by 1.15 to get 60.
2. After a 20% decrease, a quantity becomes 128. Find the original value before the change.
160
The new value is 80% of the original. Divide 128 by 0.8 to get 160.
3. After a 50% increase, a quantity becomes 120. Find the original value before the change.
80
The new value is 150% of the original. Divide 120 by 1.5 to get 80.
4. After a 30% increase, a quantity becomes 338. Find the original value before the change.
260
The new value is 130% of the original. Divide 338 by 1.3 to get 260.
5. After a 20% increase, a quantity becomes 216. Find the original value before the change.
180
The new value is 120% of the original. Divide 216 by 1.2 to get 180.
6. After a 10% decrease, a quantity becomes 270. Find the original value before the change.
300
The new value is 90% of the original. Divide 270 by 0.9 to get 300.
7. After a 40% decrease, a quantity becomes 192. Find the original value before the change.
320
The new value is 60% of the original. Divide 192 by 0.6 to get 320.
8. After a 40% decrease, a quantity becomes 252. Find the original value before the change.
420
The new value is 60% of the original. Divide 252 by 0.6 to get 420.
9. After a 20% increase, a quantity becomes 168. Find the original value before the change.
140
The new value is 120% of the original. Divide 168 by 1.2 to get 140.
10. After a 25% decrease, a quantity becomes 90. Find the original value before the change.
120
The new value is 75% of the original. Divide 90 by 0.75 to get 120.
11. After a 30% decrease, a quantity becomes 168. Find the original value before the change.
240
The new value is 70% of the original. Divide 168 by 0.7 to get 240.
12. After a 25% decrease, a quantity becomes 240. Find the original value before the change.
320
The new value is 75% of the original. Divide 240 by 0.75 to get 320.

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Reverse percentages: original value

Take your time. Show your thinking.

1. After a 15% increase, a quantity becomes 69. Find the original value before the change.
115% = 69 · 100% Original = ?
2. After a 20% decrease, a quantity becomes 128. Find the original value before the change.
80% = 128 · 100% Original = ?
3. After a 50% increase, a quantity becomes 120. Find the original value before the change.
150% = 120 · 100% Original = ?
4. After a 30% increase, a quantity becomes 338. Find the original value before the change.
130% = 338 · 100% Original = ?
5. After a 20% increase, a quantity becomes 216. Find the original value before the change.
120% = 216 · 100% Original = ?
6. After a 10% decrease, a quantity becomes 270. Find the original value before the change.
90% = 270 · 100% Original = ?
7. After a 40% decrease, a quantity becomes 192. Find the original value before the change.
60% = 192 · 100% Original = ?
8. After a 40% decrease, a quantity becomes 252. Find the original value before the change.
60% = 252 · 100% Original = ?
9. After a 20% increase, a quantity becomes 168. Find the original value before the change.
120% = 168 · 100% Original = ?
10. After a 25% decrease, a quantity becomes 90. Find the original value before the change.
75% = 90 · 100% Original = ?
11. After a 30% decrease, a quantity becomes 168. Find the original value before the change.
70% = 168 · 100% Original = ?
12. After a 25% decrease, a quantity becomes 240. Find the original value before the change.
75% = 240 · 100% Original = ?

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Reverse percentages: original value

Answers and reasoning. Review before teaching.

1. After a 15% increase, a quantity becomes 69. Find the original value before the change.
60
The new value is 115% of the original. Divide 69 by 1.15 to get 60.
2. After a 20% decrease, a quantity becomes 128. Find the original value before the change.
160
The new value is 80% of the original. Divide 128 by 0.8 to get 160.
3. After a 50% increase, a quantity becomes 120. Find the original value before the change.
80
The new value is 150% of the original. Divide 120 by 1.5 to get 80.
4. After a 30% increase, a quantity becomes 338. Find the original value before the change.
260
The new value is 130% of the original. Divide 338 by 1.3 to get 260.
5. After a 20% increase, a quantity becomes 216. Find the original value before the change.
180
The new value is 120% of the original. Divide 216 by 1.2 to get 180.
6. After a 10% decrease, a quantity becomes 270. Find the original value before the change.
300
The new value is 90% of the original. Divide 270 by 0.9 to get 300.
7. After a 40% decrease, a quantity becomes 192. Find the original value before the change.
320
The new value is 60% of the original. Divide 192 by 0.6 to get 320.
8. After a 40% decrease, a quantity becomes 252. Find the original value before the change.
420
The new value is 60% of the original. Divide 252 by 0.6 to get 420.
9. After a 20% increase, a quantity becomes 168. Find the original value before the change.
140
The new value is 120% of the original. Divide 168 by 1.2 to get 140.
10. After a 25% decrease, a quantity becomes 90. Find the original value before the change.
120
The new value is 75% of the original. Divide 90 by 0.75 to get 120.
11. After a 30% decrease, a quantity becomes 168. Find the original value before the change.
240
The new value is 70% of the original. Divide 168 by 0.7 to get 240.
12. After a 25% decrease, a quantity becomes 240. Find the original value before the change.
320
The new value is 75% of the original. Divide 240 by 0.75 to get 320.

12 questions · Seed 45 · Age guidance, not curriculum certification