Question

Given $x$ is $50\%$ larger than $z$ and $y$ is $25\%$ larger than $z$. Then, $x$ is what percent larger than $y$?

• A. $20\%$
• B. $15\%$
• C. $25\%$
• D. $37.5\%$

Answer 1

The correct option is A $20\%$

$x=\frac{150}{100}z$ (since x is 50% larger than z)
$y=\frac{125}{100}z$ (since y is 25% larger than z)
$\frac{x}{y}=\left(\frac{\frac{150}{100}}{\frac{125}{100}}\right)=\frac{150}{100}=\frac{6}{5}=1.2$
$\therefore x=1.2y=\frac{120}{100}y$
Therefore, x is 20% larger than y.