$1 \cdot 107$ If $m$ people can complete a job in $d$ days, then $m+r$ people can complete the same job in $n$ days, then $n$ is
(A) $d+r$ days.
(B) $d-r$ days.
(C) $\frac{m d}{m+r}$ days.
(D) $\frac{d}{m+r}$ days.
(E) None of the above answers is correct.
(1st American High School Mathematics Examination, 1950)
[Solution] Suppose each person can complete $\frac{1}{m d}$ of the entire work per day, and later suppose each person can complete $\frac{1}{n(m+r)}$ of the entire work per day.
$$
\therefore \quad \frac{1}{m d}=\frac{1}{(m+r) n} \text {, which gives } n=\frac{m d}{m+r} \text { (days). }
$$

Therefore, the correct choice is $(C)$.