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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 10-12Ages 13-15

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Worksheet StudioPractice pack · Ages 13-15

Reverse percentages: original value

Take your time. Show your thinking.

  1. 1. After a 30% decrease, a quantity becomes 42. Find the original value before the change.

    70% = 42 · 100% Original = ?

  2. 2. After a 40% decrease, a quantity becomes 180. Find the original value before the change.

    60% = 180 · 100% Original = ?

  3. 3. After a 15% increase, a quantity becomes 115. Find the original value before the change.

    115% = 115 · 100% Original = ?

  4. 4. After a 50% increase, a quantity becomes 180. Find the original value before the change.

    150% = 180 · 100% Original = ?

  5. 5. After a 20% decrease, a quantity becomes 256. Find the original value before the change.

    80% = 256 · 100% Original = ?

  6. 6. After a 50% increase, a quantity becomes 540. Find the original value before the change.

    150% = 540 · 100% Original = ?

  7. 7. After a 20% decrease, a quantity becomes 416. Find the original value before the change.

    80% = 416 · 100% Original = ?

  8. 8. After a 20% decrease, a quantity becomes 400. Find the original value before the change.

    80% = 400 · 100% Original = ?

  9. 9. After a 25% decrease, a quantity becomes 360. Find the original value before the change.

    75% = 360 · 100% Original = ?

  10. 10. After a 40% decrease, a quantity becomes 360. Find the original value before the change.

    60% = 360 · 100% Original = ?

  11. 11. After a 25% decrease, a quantity becomes 345. Find the original value before the change.

    75% = 345 · 100% Original = ?

  12. 12. After a 30% increase, a quantity becomes 546. Find the original value before the change.

    130% = 546 · 100% Original = ?
12 questions · Seed 50 · 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. 1. After a 30% decrease, a quantity becomes 42. Find the original value before the change.

    60

    The new value is 70% of the original. Divide 42 by 0.7 to get 60.

  2. 2. After a 40% decrease, a quantity becomes 180. Find the original value before the change.

    300

    The new value is 60% of the original. Divide 180 by 0.6 to get 300.

  3. 3. After a 15% increase, a quantity becomes 115. Find the original value before the change.

    100

    The new value is 115% of the original. Divide 115 by 1.15 to get 100.

  4. 4. After a 50% increase, a quantity becomes 180. Find the original value before the change.

    120

    The new value is 150% of the original. Divide 180 by 1.5 to get 120.

  5. 5. After a 20% decrease, a quantity becomes 256. Find the original value before the change.

    320

    The new value is 80% of the original. Divide 256 by 0.8 to get 320.

  6. 6. After a 50% increase, a quantity becomes 540. Find the original value before the change.

    360

    The new value is 150% of the original. Divide 540 by 1.5 to get 360.

  7. 7. After a 20% decrease, a quantity becomes 416. Find the original value before the change.

    520

    The new value is 80% of the original. Divide 416 by 0.8 to get 520.

  8. 8. After a 20% decrease, a quantity becomes 400. Find the original value before the change.

    500

    The new value is 80% of the original. Divide 400 by 0.8 to get 500.

  9. 9. After a 25% decrease, a quantity becomes 360. Find the original value before the change.

    480

    The new value is 75% of the original. Divide 360 by 0.75 to get 480.

  10. 10. After a 40% decrease, a quantity becomes 360. Find the original value before the change.

    600

    The new value is 60% of the original. Divide 360 by 0.6 to get 600.

  11. 11. After a 25% decrease, a quantity becomes 345. Find the original value before the change.

    460

    The new value is 75% of the original. Divide 345 by 0.75 to get 460.

  12. 12. After a 30% increase, a quantity becomes 546. Find the original value before the change.

    420

    The new value is 130% of the original. Divide 546 by 1.3 to get 420.

12 questions · Seed 50 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Reverse percentages: original value

Take your time. Show your thinking.

  1. 1. After a 30% decrease, a quantity becomes 42. Find the original value before the change.

    70% = 42 · 100% Original = ?

  2. 2. After a 40% decrease, a quantity becomes 180. Find the original value before the change.

    60% = 180 · 100% Original = ?

  3. 3. After a 15% increase, a quantity becomes 115. Find the original value before the change.

    115% = 115 · 100% Original = ?

  4. 4. After a 50% increase, a quantity becomes 180. Find the original value before the change.

    150% = 180 · 100% Original = ?

  5. 5. After a 20% decrease, a quantity becomes 256. Find the original value before the change.

    80% = 256 · 100% Original = ?

  6. 6. After a 50% increase, a quantity becomes 540. Find the original value before the change.

    150% = 540 · 100% Original = ?

  7. 7. After a 20% decrease, a quantity becomes 416. Find the original value before the change.

    80% = 416 · 100% Original = ?

  8. 8. After a 20% decrease, a quantity becomes 400. Find the original value before the change.

    80% = 400 · 100% Original = ?

  9. 9. After a 25% decrease, a quantity becomes 360. Find the original value before the change.

    75% = 360 · 100% Original = ?

  10. 10. After a 40% decrease, a quantity becomes 360. Find the original value before the change.

    60% = 360 · 100% Original = ?

  11. 11. After a 25% decrease, a quantity becomes 345. Find the original value before the change.

    75% = 345 · 100% Original = ?

  12. 12. After a 30% increase, a quantity becomes 546. Find the original value before the change.

    130% = 546 · 100% Original = ?
12 questions · Seed 50 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Reverse percentages: original value

Answers and reasoning. Review before teaching.

  1. 1. After a 30% decrease, a quantity becomes 42. Find the original value before the change.

    60

    The new value is 70% of the original. Divide 42 by 0.7 to get 60.

  2. 2. After a 40% decrease, a quantity becomes 180. Find the original value before the change.

    300

    The new value is 60% of the original. Divide 180 by 0.6 to get 300.

  3. 3. After a 15% increase, a quantity becomes 115. Find the original value before the change.

    100

    The new value is 115% of the original. Divide 115 by 1.15 to get 100.

  4. 4. After a 50% increase, a quantity becomes 180. Find the original value before the change.

    120

    The new value is 150% of the original. Divide 180 by 1.5 to get 120.

  5. 5. After a 20% decrease, a quantity becomes 256. Find the original value before the change.

    320

    The new value is 80% of the original. Divide 256 by 0.8 to get 320.

  6. 6. After a 50% increase, a quantity becomes 540. Find the original value before the change.

    360

    The new value is 150% of the original. Divide 540 by 1.5 to get 360.

  7. 7. After a 20% decrease, a quantity becomes 416. Find the original value before the change.

    520

    The new value is 80% of the original. Divide 416 by 0.8 to get 520.

  8. 8. After a 20% decrease, a quantity becomes 400. Find the original value before the change.

    500

    The new value is 80% of the original. Divide 400 by 0.8 to get 500.

  9. 9. After a 25% decrease, a quantity becomes 360. Find the original value before the change.

    480

    The new value is 75% of the original. Divide 360 by 0.75 to get 480.

  10. 10. After a 40% decrease, a quantity becomes 360. Find the original value before the change.

    600

    The new value is 60% of the original. Divide 360 by 0.6 to get 600.

  11. 11. After a 25% decrease, a quantity becomes 345. Find the original value before the change.

    460

    The new value is 75% of the original. Divide 345 by 0.75 to get 460.

  12. 12. After a 30% increase, a quantity becomes 546. Find the original value before the change.

    420

    The new value is 130% of the original. Divide 546 by 1.3 to get 420.

12 questions · Seed 50 · Age guidance, not curriculum certification