If $x$ and $y$ are positive numbers and the average of 4, 20 and $x$ is equal to the average of $y$ and 16 , then the ratio $x: y$ is
(A) $3: 2$
(B) 2:3
(C) $1: 1$
(D) $2: 5$
(E) 5:2
The average of 4,20 and $x$ is equal to $\frac{4+20+x}{3}$. The average of $y$ and 16 is equal to $\frac{16+y}{2}$.

Since these averages are equal,

$$
\begin{aligned}
\frac{4+20+x}{3} & =\frac{16+y}{2} \\
2(4+20+x) & =3(16+y) \\
48+2 x & =48+3 y \\
2 x & =3 y \\
\frac{x}{y} & =\frac{3}{2}
\end{aligned}
$$

Answer: (A)