3.7 The difference of two numbers, the ratio of their sum and product is $1: 7: 24$, then the product of these two numbers is
(A) 6.
(B) 12.
(C) 24.
(D) 48.
(E) 96.
(15th American High School Mathematics Examination, 1964)
[Solution] Let the two numbers be $x, y$. According to the problem, we have
$$
\left\{\begin{array}{l}
x + y = 7 ( x - y ), \\
x y = 24 ( x - y );
\end{array} \text { i.e., } \quad \left\{\begin{array}{l}
8 y - 6 x = 0, \\
x y - 24 x + 24 y = 0 .
\end{array}\right.\right.
$$

Substituting the first equation of the latter set into the second equation, we get $x(y-6)=0$, which gives
$$
x=0 \quad \text { or } y=6 \text {. }
$$
$x=0$ does not satisfy the problem, so $y=6$. Thus, $x=8$.
$\therefore$
$$
x y = 48 \text {. }
$$

Therefore, the answer is $(D)$.