Why?

This common math riddle can puzzle many at first glance: if you increase a number by 15% and then decrease the result by 15%, why is the final number smaller than the original? The key lies in understanding how percentages work on changing bases rather than fixed amounts. When you increase the original number by 15%, you multiply it by 1.15. However, when you then decrease the new number by 15%, you are reducing 15% of the increased value, not the original. Specifically, you multiply by 0.85 (which is 100% - 15%) of the bigger number. Mathematically, if the original number is N, after the increase it's N × 1.15. After the decrease, it's (N × 1.15) × 0.85 = N × 0.9775. Notice that 0.9775 is less than 1, meaning the final result is about 97.75% of the original number N, hence smaller. This illustrates an important concept in percentage calculations: percentage increase and decrease are not directly reversible because they operate on different amounts. It's a useful insight for financial calculations, discounts, and price changes where percentages apply sequentially. Personally, I first learned about this riddle during school and it shaped how I approach real-world problems involving percentages. Understanding this helped me avoid common errors in budgeting and sales calculations. If you’re learning math or helping students, explaining this with simple numbers can make the idea click quickly. For example, start with 100 as the original value, increase by 15% to get 115, then decrease by 15% of 115 (which is 17.25), resulting in 97.75 — clearly less than the initial 100. Overall, this riddle is a great exercise to develop a deeper understanding of percentage operations beyond simple increases or decreases, especially useful for students and anyone dealing with percentage calculations in school or everyday life.