Question

假设 $A > B > 0$ ，且 $A$ 比 $B$ 大 $x\%$ 。求 $x$ 。

Suppose $A > B > 0$ and $A$ is $x\%$ greater than $B.$ What is $x?$

$100\left(\frac{A-B}{B}\right)$

$100\left(\frac{A+B}{B}\right)$

$100\left(\frac{A+B}{A}\right)$

$100\left(\frac{A-B}{A}\right)$

$100\left(\frac{A}{B}\right)$

$A = \dfrac {x+ 100}{100}B$ $= B + \dfrac x{100}B.$

根据百分比增加的定义， $\begin{aligned} (A-B) &= \dfrac x{100}B\\ 100\left(\dfrac{A-B} B\right) &=x.\end{aligned}$

所以正确答案是 A。

By definition, we know $A = \dfrac {x+ 100}{100}B$ $= B + \dfrac x{100}B.$

This implies, $\begin{aligned} (A-B) &= \dfrac x{100}B\\ 100\left(\dfrac{A-B} B\right) &=x.\end{aligned}$

Thus, the correct answer is A .