2.8 In a crowd, if 15 women leave, the remaining ratio of men to women is $2: 1$; after this, if 45 men leave, the ratio of men to women becomes $1: 5$. How many women were there initially?
(A) 40.
(B) 43.
(C) 29.
(D) 50.
(E) None of the above answers is correct.
(1st American High School Mathematics Examination, 1950)
[Solution] Let the initial number of women be $x$, then according to the problem, the number of men is $2(x-15)$. From the problem, we have

Solving gives
$$
\begin{array}{c}
5[2(x-15)-45]=x-15, \\
x=40 .
\end{array}
$$

Therefore, the answer is $(A)$.