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 198. Find the original value before the change.
110% = 198 · 100% Original = ?
2. After a 50% increase, a quantity becomes 270. Find the original value before the change.
150% = 270 · 100% Original = ?
3. After a 30% decrease, a quantity becomes 266. Find the original value before the change.
70% = 266 · 100% Original = ?
4. After a 25% increase, a quantity becomes 575. Find the original value before the change.
125% = 575 · 100% Original = ?
5. After a 40% increase, a quantity becomes 280. Find the original value before the change.
140% = 280 · 100% Original = ?
6. After a 15% increase, a quantity becomes 483. Find the original value before the change.
115% = 483 · 100% Original = ?
7. After a 40% decrease, a quantity becomes 144. Find the original value before the change.
60% = 144 · 100% Original = ?
8. After a 40% increase, a quantity becomes 812. Find the original value before the change.
140% = 812 · 100% Original = ?
9. After a 30% increase, a quantity becomes 754. Find the original value before the change.
130% = 754 · 100% Original = ?
10. After a 10% increase, a quantity becomes 220. Find the original value before the change.
110% = 220 · 100% Original = ?
11. After a 30% increase, a quantity becomes 104. Find the original value before the change.
130% = 104 · 100% Original = ?
12. After a 20% decrease, a quantity becomes 160. Find the original value before the change.
80% = 160 · 100% Original = ?

12 questions · Seed 47 · 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 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.
2. After a 50% increase, a quantity becomes 270. Find the original value before the change.
180
The new value is 150% of the original. Divide 270 by 1.5 to get 180.
3. After a 30% decrease, a quantity becomes 266. Find the original value before the change.
380
The new value is 70% of the original. Divide 266 by 0.7 to get 380.
4. After a 25% increase, a quantity becomes 575. Find the original value before the change.
460
The new value is 125% of the original. Divide 575 by 1.25 to get 460.
5. After a 40% increase, a quantity becomes 280. Find the original value before the change.
200
The new value is 140% of the original. Divide 280 by 1.4 to get 200.
6. After a 15% increase, a quantity becomes 483. Find the original value before the change.
420
The new value is 115% of the original. Divide 483 by 1.15 to get 420.
7. After a 40% decrease, a quantity becomes 144. Find the original value before the change.
240
The new value is 60% of the original. Divide 144 by 0.6 to get 240.
8. After a 40% increase, a quantity becomes 812. Find the original value before the change.
580
The new value is 140% of the original. Divide 812 by 1.4 to get 580.
9. After a 30% increase, a quantity becomes 754. Find the original value before the change.
580
The new value is 130% of the original. Divide 754 by 1.3 to get 580.
10. After a 10% increase, a quantity becomes 220. Find the original value before the change.
200
The new value is 110% of the original. Divide 220 by 1.1 to get 200.
11. After a 30% increase, a quantity becomes 104. Find the original value before the change.
80
The new value is 130% of the original. Divide 104 by 1.3 to get 80.
12. After a 20% decrease, a quantity becomes 160. Find the original value before the change.
200
The new value is 80% of the original. Divide 160 by 0.8 to get 200.

12 questions · Seed 47 · 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 198. Find the original value before the change.
110% = 198 · 100% Original = ?
2. After a 50% increase, a quantity becomes 270. Find the original value before the change.
150% = 270 · 100% Original = ?
3. After a 30% decrease, a quantity becomes 266. Find the original value before the change.
70% = 266 · 100% Original = ?
4. After a 25% increase, a quantity becomes 575. Find the original value before the change.
125% = 575 · 100% Original = ?
5. After a 40% increase, a quantity becomes 280. Find the original value before the change.
140% = 280 · 100% Original = ?
6. After a 15% increase, a quantity becomes 483. Find the original value before the change.
115% = 483 · 100% Original = ?
7. After a 40% decrease, a quantity becomes 144. Find the original value before the change.
60% = 144 · 100% Original = ?
8. After a 40% increase, a quantity becomes 812. Find the original value before the change.
140% = 812 · 100% Original = ?
9. After a 30% increase, a quantity becomes 754. Find the original value before the change.
130% = 754 · 100% Original = ?
10. After a 10% increase, a quantity becomes 220. Find the original value before the change.
110% = 220 · 100% Original = ?
11. After a 30% increase, a quantity becomes 104. Find the original value before the change.
130% = 104 · 100% Original = ?
12. After a 20% decrease, a quantity becomes 160. Find the original value before the change.
80% = 160 · 100% Original = ?

12 questions · Seed 47 · 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 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.
2. After a 50% increase, a quantity becomes 270. Find the original value before the change.
180
The new value is 150% of the original. Divide 270 by 1.5 to get 180.
3. After a 30% decrease, a quantity becomes 266. Find the original value before the change.
380
The new value is 70% of the original. Divide 266 by 0.7 to get 380.
4. After a 25% increase, a quantity becomes 575. Find the original value before the change.
460
The new value is 125% of the original. Divide 575 by 1.25 to get 460.
5. After a 40% increase, a quantity becomes 280. Find the original value before the change.
200
The new value is 140% of the original. Divide 280 by 1.4 to get 200.
6. After a 15% increase, a quantity becomes 483. Find the original value before the change.
420
The new value is 115% of the original. Divide 483 by 1.15 to get 420.
7. After a 40% decrease, a quantity becomes 144. Find the original value before the change.
240
The new value is 60% of the original. Divide 144 by 0.6 to get 240.
8. After a 40% increase, a quantity becomes 812. Find the original value before the change.
580
The new value is 140% of the original. Divide 812 by 1.4 to get 580.
9. After a 30% increase, a quantity becomes 754. Find the original value before the change.
580
The new value is 130% of the original. Divide 754 by 1.3 to get 580.
10. After a 10% increase, a quantity becomes 220. Find the original value before the change.
200
The new value is 110% of the original. Divide 220 by 1.1 to get 200.
11. After a 30% increase, a quantity becomes 104. Find the original value before the change.
80
The new value is 130% of the original. Divide 104 by 1.3 to get 80.
12. After a 20% decrease, a quantity becomes 160. Find the original value before the change.
200
The new value is 80% of the original. Divide 160 by 0.8 to get 200.

12 questions · Seed 47 · Age guidance, not curriculum certification