The two whole numbers $m$ and $n$ satisfy $m+n=20$ and $\frac{1}{m}+\frac{1}{n}=\frac{5}{24}$. The product $m n$ is equal to
(A) 72
(B) 36
(C) 48
(D) 96
(E) 24
Putting each of the two fractions over a common denominator of $m n$, we get

$$
\begin{aligned}
\frac{1}{m}+\frac{1}{n} & =\frac{5}{24} \\
\frac{n}{m n}+\frac{m}{m n} & =\frac{5}{24} \\
\frac{m+n}{m n} & =\frac{5}{24} \\
\frac{20}{m n} & =\frac{5}{24} \\
m n & =\frac{24 \times 20}{5} \\
m n & =96
\end{aligned}
$$

Answer: (D)