If a number $x$ is 10% less than another number $y$ and $y$ is 10% more than 125, then $x$ is equal to

### Concept & Logic This is a problem of successive percentage changes. You can trace the values sequentially or use successive multipliers to find the final value in one step. $$ x = \text{Base} \times \left(1 + \frac{R_1}{100}\right) \times \left(1 - \frac{R_2}{100}\right) $$ ### Step-by-Step Solution * **Step 1:** Find the value of $y$. We are given that $y$ is 10% more than 125. $$ y = 125 + (10\% \text{ of } 125) $$ $$ y = 125 + 12.5 = 137.5 $$ * **Step 2:** Find the value of $x$. We are given that $x$ is 10% less than $y$. $$ x = 137.5 - (10\% \text{ of } 137.5) $$ $$ x = 137.5 - 13.75 = 123.75 $$ ### Exam Strategy & Shortcut Use decimal multipliers for a faster, one-line calculation. "10% more" means multiply by $1.1$. "10% less" means multiply by $0.9$. $$ x = 125 \times 1.1 \times 0.9 $$ $$ x = 125 \times 0.99 $$ Calculating 99% of a number is just subtracting 1% of it from the original value: $$ x = 125 - 1.25 = 123.75 $$ ### Common Pitfall A very common intuition trap is assuming that a 10% increase followed by a 10% decrease cancels out, bringing the value back to the original 125. Successive identical increases and decreases always result in a net decrease (specifically, a loss of $\frac{x^2}{100}\%$). ### Final Answer **Therefore, the correct answer is 123.75.**