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 138. Find the original value before the change.
115% = 138 · 100% Original = ?
2. After a 20% decrease, a quantity becomes 432. Find the original value before the change.
80% = 432 · 100% Original = ?
3. After a 40% decrease, a quantity becomes 300. Find the original value before the change.
60% = 300 · 100% Original = ?
4. After a 25% decrease, a quantity becomes 180. Find the original value before the change.
75% = 180 · 100% Original = ?
5. After a 30% increase, a quantity becomes 312. Find the original value before the change.
130% = 312 · 100% Original = ?
6. After a 40% increase, a quantity becomes 420. Find the original value before the change.
140% = 420 · 100% Original = ?
7. After a 10% decrease, a quantity becomes 216. Find the original value before the change.
90% = 216 · 100% Original = ?
8. After a 30% increase, a quantity becomes 520. Find the original value before the change.
130% = 520 · 100% Original = ?
9. After a 40% increase, a quantity becomes 588. Find the original value before the change.
140% = 588 · 100% Original = ?
10. After a 15% decrease, a quantity becomes 119. Find the original value before the change.
85% = 119 · 100% Original = ?
11. After a 50% decrease, a quantity becomes 20. Find the original value before the change.
50% = 20 · 100% Original = ?
12. After a 30% decrease, a quantity becomes 420. Find the original value before the change.
70% = 420 · 100% Original = ?

12 questions · Seed 42 · 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 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.
2. After a 20% decrease, a quantity becomes 432. Find the original value before the change.
540
The new value is 80% of the original. Divide 432 by 0.8 to get 540.
3. 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.
4. After a 25% decrease, a quantity becomes 180. Find the original value before the change.
240
The new value is 75% of the original. Divide 180 by 0.75 to get 240.
5. After a 30% increase, a quantity becomes 312. Find the original value before the change.
240
The new value is 130% of the original. Divide 312 by 1.3 to get 240.
6. After a 40% increase, a quantity becomes 420. Find the original value before the change.
300
The new value is 140% of the original. Divide 420 by 1.4 to get 300.
7. After a 10% decrease, a quantity becomes 216. Find the original value before the change.
240
The new value is 90% of the original. Divide 216 by 0.9 to get 240.
8. After a 30% increase, a quantity becomes 520. Find the original value before the change.
400
The new value is 130% of the original. Divide 520 by 1.3 to get 400.
9. After a 40% increase, a quantity becomes 588. Find the original value before the change.
420
The new value is 140% of the original. Divide 588 by 1.4 to get 420.
10. After a 15% decrease, a quantity becomes 119. Find the original value before the change.
140
The new value is 85% of the original. Divide 119 by 0.85 to get 140.
11. After a 50% decrease, a quantity becomes 20. Find the original value before the change.
40
The new value is 50% of the original. Divide 20 by 0.5 to get 40.
12. After a 30% decrease, a quantity becomes 420. Find the original value before the change.
600
The new value is 70% of the original. Divide 420 by 0.7 to get 600.

12 questions · Seed 42 · 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 138. Find the original value before the change.
115% = 138 · 100% Original = ?
2. After a 20% decrease, a quantity becomes 432. Find the original value before the change.
80% = 432 · 100% Original = ?
3. After a 40% decrease, a quantity becomes 300. Find the original value before the change.
60% = 300 · 100% Original = ?
4. After a 25% decrease, a quantity becomes 180. Find the original value before the change.
75% = 180 · 100% Original = ?
5. After a 30% increase, a quantity becomes 312. Find the original value before the change.
130% = 312 · 100% Original = ?
6. After a 40% increase, a quantity becomes 420. Find the original value before the change.
140% = 420 · 100% Original = ?
7. After a 10% decrease, a quantity becomes 216. Find the original value before the change.
90% = 216 · 100% Original = ?
8. After a 30% increase, a quantity becomes 520. Find the original value before the change.
130% = 520 · 100% Original = ?
9. After a 40% increase, a quantity becomes 588. Find the original value before the change.
140% = 588 · 100% Original = ?
10. After a 15% decrease, a quantity becomes 119. Find the original value before the change.
85% = 119 · 100% Original = ?
11. After a 50% decrease, a quantity becomes 20. Find the original value before the change.
50% = 20 · 100% Original = ?
12. After a 30% decrease, a quantity becomes 420. Find the original value before the change.
70% = 420 · 100% Original = ?

12 questions · Seed 42 · 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 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.
2. After a 20% decrease, a quantity becomes 432. Find the original value before the change.
540
The new value is 80% of the original. Divide 432 by 0.8 to get 540.
3. 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.
4. After a 25% decrease, a quantity becomes 180. Find the original value before the change.
240
The new value is 75% of the original. Divide 180 by 0.75 to get 240.
5. After a 30% increase, a quantity becomes 312. Find the original value before the change.
240
The new value is 130% of the original. Divide 312 by 1.3 to get 240.
6. After a 40% increase, a quantity becomes 420. Find the original value before the change.
300
The new value is 140% of the original. Divide 420 by 1.4 to get 300.
7. After a 10% decrease, a quantity becomes 216. Find the original value before the change.
240
The new value is 90% of the original. Divide 216 by 0.9 to get 240.
8. After a 30% increase, a quantity becomes 520. Find the original value before the change.
400
The new value is 130% of the original. Divide 520 by 1.3 to get 400.
9. After a 40% increase, a quantity becomes 588. Find the original value before the change.
420
The new value is 140% of the original. Divide 588 by 1.4 to get 420.
10. After a 15% decrease, a quantity becomes 119. Find the original value before the change.
140
The new value is 85% of the original. Divide 119 by 0.85 to get 140.
11. After a 50% decrease, a quantity becomes 20. Find the original value before the change.
40
The new value is 50% of the original. Divide 20 by 0.5 to get 40.
12. After a 30% decrease, a quantity becomes 420. Find the original value before the change.
600
The new value is 70% of the original. Divide 420 by 0.7 to get 600.

12 questions · Seed 42 · Age guidance, not curriculum certification