A number is increased by 20% and then decreased by 20%. If the final result is 96, what was the original number?

Tue, 05 May 2026 09:31:44 +0000

**Why Does a Number Increase by 20% and Then Decrease by 20% End Up Lower Than It Started? The 96-Clue Puzzle** In the fast-evolving digital landscape, a simple math pattern is sparking curiosity: what happens when a number grows by 20%, then shrinks by the same percentage? The logical question has surfaced widely—especially in economic, financial, and data-driven conversations across the U.S. audience. Many wonder: if a number ends up at 96 after a 20% increase followed by a 20% decrease, what was the original value? This isn’t just a classroom example—it’s a pattern appearing in discussions around inflation adjustments, performance metrics, and financial modeling. Understanding the math behind this loop reveals important insights into percentage changes and common misconceptions. ### How a 20% Increase Followed by a 20% Decrease Actually Lowers the Base When a number grows by 20%, it becomes 1.2 times the original value. But when it drops by 20% afterward, it shrinks to 80% of the new value—not 80% of the starting number. Let’s break it down mathematically. If the original number is *X*, after a 20% increase:
**Increased value = X × 1.2**
Then reducing this by 20% results in:
**Final value = (X × 1.2) × 0.8 = X × 0.96**
This shows the final result equals 96% of the original number—not the same as the starting value. So, if 96 is the end result, the original number must be:
**X = 96 ÷ 0.96 = 100**