← Section 3 Chapter 29: Reverse Percentage Problems Chapter 30 →

🔄 Reverse Percentage Problems

Sometimes you know the final amount and the percentage change, but need to find the original amount

🎯 What You'll Learn

  • Find original values after percentage increases or decreases
  • Work backwards from final amounts
  • Use multipliers to solve reverse percentage problems
  • Apply reverse percentages to real-world situations

✏️ Explanation

Sometimes you know the final amount and the percentage change, but need to find the original amount.

🔍 Why It Matters

Useful for finding original prices before discounts, or initial values before growth. Essential for solving real-world problems where you know the result but need the starting point.

🧭 Reverse Percentage Solver

📈 Forward Percentage
We know: Original value and percentage change
We find: Final value

Method: Multiply by the decimal
£100 + 20% = £100 × 1.2 = £120
VS
🔄 Reverse Percentage
We know: Final value and percentage change
We find: Original value

Method: Divide by the decimal
£120 after 20% increase = £120 ÷ 1.2 = £100

✏️ Worked Example: After 20% increase, price is £36

Given: After a 20% increase, a price is now £36. What was the original price?
Step 1: Identify what percentage the final amount represents
20% increase means final = 120% of original
Step 2: Convert to decimal multiplier
120% = 1.2
Step 3: Divide to find original
Original = £36 ÷ 1.2 = £30
Answer: The original price was £30

🧮 Interactive Reverse Percentage Solver

After a 20% increase, the value is £120. What was the original value?
Original Value:
£100.00
1
Identify the multiplier
20% increase means final value is 120% of original
2
Convert to decimal
120% = 1.2
3
Divide to find original
Original = £120 ÷ 1.2 = £100.00
4
Check your answer
£100.00 + 20% = £120 ✓

🔢 Practice Exercises

1. After 15% discount, price is £85. Find original price.
£
2. After 25% increase, population is 1500. Find original.
3. After 10% decrease, mass is 90kg. Find original mass.
kg
4. After 30% discount, cost is £14. Find original cost.
£
5. After 5% increase, length is 21cm. Find original length.
cm

⚠️ Common Mistakes

  • Adding/subtracting percentage instead of using multipliers
  • Using wrong percentage (e.g., 20% instead of 120%)
  • Forgetting to convert percentage to decimal before dividing

✨ Quick Summary

Work backwards using multipliers. New amount ÷ multiplier = original.