A number is increased by 20% and then decreased by 25%. If the final result is 90, what was the original number?
["How to Find the Original Number When It’s Increased by 20% Then Decreased by 25% – A Step-by-Step Solution", "Understanding how numbers change through percentage increases and decreases is essential in math, finance, and everyday problem-solving. In this article, we’ll explore a common scenario: a number increases by 20%, then decreases by 25%, resulting in a final value of 90. We’ll break down the calculation clearly and explain how to reverse these operations to find the original number.", "---", "## The Problem", "A number is increased by 20%, then decreased by 25%. The final result is 90. What was the original number?", "---", "## Step-by-Step Explanation", "Let the original number be x.", "### Step 1: Increase by 20%\nA 20% increase means multiplying x by (1 + 0.20) = 1.20.\nAfter the increase:\n[\nx \ imes 1.20 = 1.2x\n]", "### Step 2: Decrease by 25%\nA 25% decrease means multiplying the new value by (1 – 0.25) = 0.75.\nAfter the decrease:\n[\n1.2x \ imes 0.75 = 0.9x\n]", "We’re told that final result equals 90:\n[\n0.9x = 90\n]", "### Step 3: Solve for x\nTo find x, divide both sides by 0.9:\n[\nx = \frac{90}{0.9} = 100\n]", "---", "## Final Answer", "The original number is 100.", "---", "## Why This Matters", "This type of problem enhances your ability to work with percentage changes—common in discounts, interest calculations, and data analysis. Knowing how to reverse percentage adjustments helps solve real-world challenges efficiently.", "---", "## Summary", "- Original number: x\n- After 20% increase: 1.2x\n- After 25% decrease: 0.9x\n- Given final value = 90 → 0.9x = 90\n- x = 100", "By following these clear mathematical steps, you can easily reverse any two-step percentage operation to uncover the original value.", "---", "Keywords: original number percentage increase 20%, percentage decrease 25%, solve percentage change, how to find original number after adjustments, step-by-step math problem, percentage calculation guide."]
