CEMC Cayley, 2022

Solution 1

Since $x$ is $20\%$ of $y$, then $x = \frac{20}{100}y = \frac{1}{5}y$.

Since $x$ is $50\%$ of $z$, then $x = \frac{1}{2}z$.

Therefore, $\frac{1}{5}y = \frac{1}{2}z$ which gives $\frac{2}{5}y = z$.

Thus, $z = \frac{40}{100}y$ and so
$z$ is 40% of $y$.

Solution 2 Since $x$ is
$20\%$ of $y$, then $x = 0.2y$.

Since $x$ is $50\%$ of $z$, then $x = 0.5z$.

Therefore, $0.2y = 0.5z$ which gives
$0.4y = z$.

Thus, $z = 0.4y$ and so $z$ is $40\%$ of $y$.