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 20% increase, a quantity becomes 696. Find the original value before the change.
120% = 696 · 100% Original = ?
2. After a 20% increase, a quantity becomes 360. Find the original value before the change.
120% = 360 · 100% Original = ?
3. After a 30% decrease, a quantity becomes 308. Find the original value before the change.
70% = 308 · 100% Original = ?
4. After a 50% decrease, a quantity becomes 70. Find the original value before the change.
50% = 70 · 100% Original = ?
5. After a 20% increase, a quantity becomes 192. Find the original value before the change.
120% = 192 · 100% Original = ?
6. After a 15% increase, a quantity becomes 322. Find the original value before the change.
115% = 322 · 100% Original = ?
7. After a 30% decrease, a quantity becomes 98. Find the original value before the change.
70% = 98 · 100% Original = ?
8. After a 15% increase, a quantity becomes 437. Find the original value before the change.
115% = 437 · 100% Original = ?
9. After a 10% decrease, a quantity becomes 216. Find the original value before the change.
90% = 216 · 100% Original = ?
10. After a 15% increase, a quantity becomes 575. Find the original value before the change.
115% = 575 · 100% Original = ?
11. After a 50% increase, a quantity becomes 450. Find the original value before the change.
150% = 450 · 100% Original = ?
12. After a 15% decrease, a quantity becomes 289. Find the original value before the change.
85% = 289 · 100% Original = ?

12 questions · Seed 48 · 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 20% increase, a quantity becomes 696. Find the original value before the change.
580
The new value is 120% of the original. Divide 696 by 1.2 to get 580.
2. After a 20% increase, a quantity becomes 360. Find the original value before the change.
300
The new value is 120% of the original. Divide 360 by 1.2 to get 300.
3. After a 30% decrease, a quantity becomes 308. Find the original value before the change.
440
The new value is 70% of the original. Divide 308 by 0.7 to get 440.
4. After a 50% decrease, a quantity becomes 70. Find the original value before the change.
140
The new value is 50% of the original. Divide 70 by 0.5 to get 140.
5. After a 20% increase, a quantity becomes 192. Find the original value before the change.
160
The new value is 120% of the original. Divide 192 by 1.2 to get 160.
6. After a 15% increase, a quantity becomes 322. Find the original value before the change.
280
The new value is 115% of the original. Divide 322 by 1.15 to get 280.
7. After a 30% decrease, a quantity becomes 98. Find the original value before the change.
140
The new value is 70% of the original. Divide 98 by 0.7 to get 140.
8. After a 15% increase, a quantity becomes 437. Find the original value before the change.
380
The new value is 115% of the original. Divide 437 by 1.15 to get 380.
9. 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.
10. After a 15% increase, a quantity becomes 575. Find the original value before the change.
500
The new value is 115% of the original. Divide 575 by 1.15 to get 500.
11. After a 50% increase, a quantity becomes 450. Find the original value before the change.
300
The new value is 150% of the original. Divide 450 by 1.5 to get 300.
12. After a 15% decrease, a quantity becomes 289. Find the original value before the change.
340
The new value is 85% of the original. Divide 289 by 0.85 to get 340.

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Reverse percentages: original value

Take your time. Show your thinking.

1. After a 20% increase, a quantity becomes 696. Find the original value before the change.
120% = 696 · 100% Original = ?
2. After a 20% increase, a quantity becomes 360. Find the original value before the change.
120% = 360 · 100% Original = ?
3. After a 30% decrease, a quantity becomes 308. Find the original value before the change.
70% = 308 · 100% Original = ?
4. After a 50% decrease, a quantity becomes 70. Find the original value before the change.
50% = 70 · 100% Original = ?
5. After a 20% increase, a quantity becomes 192. Find the original value before the change.
120% = 192 · 100% Original = ?
6. After a 15% increase, a quantity becomes 322. Find the original value before the change.
115% = 322 · 100% Original = ?
7. After a 30% decrease, a quantity becomes 98. Find the original value before the change.
70% = 98 · 100% Original = ?
8. After a 15% increase, a quantity becomes 437. Find the original value before the change.
115% = 437 · 100% Original = ?
9. After a 10% decrease, a quantity becomes 216. Find the original value before the change.
90% = 216 · 100% Original = ?
10. After a 15% increase, a quantity becomes 575. Find the original value before the change.
115% = 575 · 100% Original = ?
11. After a 50% increase, a quantity becomes 450. Find the original value before the change.
150% = 450 · 100% Original = ?
12. After a 15% decrease, a quantity becomes 289. Find the original value before the change.
85% = 289 · 100% Original = ?

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Reverse percentages: original value

Answers and reasoning. Review before teaching.

1. After a 20% increase, a quantity becomes 696. Find the original value before the change.
580
The new value is 120% of the original. Divide 696 by 1.2 to get 580.
2. After a 20% increase, a quantity becomes 360. Find the original value before the change.
300
The new value is 120% of the original. Divide 360 by 1.2 to get 300.
3. After a 30% decrease, a quantity becomes 308. Find the original value before the change.
440
The new value is 70% of the original. Divide 308 by 0.7 to get 440.
4. After a 50% decrease, a quantity becomes 70. Find the original value before the change.
140
The new value is 50% of the original. Divide 70 by 0.5 to get 140.
5. After a 20% increase, a quantity becomes 192. Find the original value before the change.
160
The new value is 120% of the original. Divide 192 by 1.2 to get 160.
6. After a 15% increase, a quantity becomes 322. Find the original value before the change.
280
The new value is 115% of the original. Divide 322 by 1.15 to get 280.
7. After a 30% decrease, a quantity becomes 98. Find the original value before the change.
140
The new value is 70% of the original. Divide 98 by 0.7 to get 140.
8. After a 15% increase, a quantity becomes 437. Find the original value before the change.
380
The new value is 115% of the original. Divide 437 by 1.15 to get 380.
9. 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.
10. After a 15% increase, a quantity becomes 575. Find the original value before the change.
500
The new value is 115% of the original. Divide 575 by 1.15 to get 500.
11. After a 50% increase, a quantity becomes 450. Find the original value before the change.
300
The new value is 150% of the original. Divide 450 by 1.5 to get 300.
12. After a 15% decrease, a quantity becomes 289. Find the original value before the change.
340
The new value is 85% of the original. Divide 289 by 0.85 to get 340.

12 questions · Seed 48 · Age guidance, not curriculum certification