$1 \cdot 116$ In a group of doctors and lawyers, the average (arithmetic mean) age is 40 years. If the average age of the doctors is 35 years, and the average age of the lawyers is 50 years, then the ratio of the number of doctors to the number of lawyers is
(A) $3: 2$.
(B) $3: 1$.
(C) $2: 3$.
(D) $2: 1$.
(E) $1: 2$.
(24th American High School Mathematics Examination, 1973)
[Solution] Let $m$ and $n$ represent the number of doctors and lawyers, respectively. Then, according to the problem, we have
$$
40(m+n)=35 m+50 n,
$$

which simplifies to
$$
5 m=10 n \text { or } \frac{m}{n}=2 \text {. }
$$

The required ratio is
$$
m: n=2: 1 \text {. }
$$

Therefore, the answer is $(D)$.