1.109 If $x$ cows produce $x+1$ buckets of milk in $x+2$ days, then the number of days required for $x+3$ cows to produce $x+5$ buckets of milk is
(A) $\frac{x(x+2)(x+5)}{(x+1)(x+3)}$.
(B) $\frac{x(x+1)(x+5)}{(x+2)(x+3)}$.
(C) $\frac{(x+1)(x+3)(x+5)}{x(x+2)}$.
(D) $\frac{(x+1)(x+3)}{x(x+2)(x+5)}$.
(E) None of these.
(27th American High School Mathematics Examination, 1976)
[Solution] From the problem, we know that one cow gets $\frac{(x+1)}{x(x+2)}$ buckets of milk per day, so $(x+3)$ cows get $\frac{(x+1)(x+3)}{x(x+2)}$ buckets of milk per day.

Therefore, to get $(x+5)$ buckets of milk, it would take $\frac{x(x+2)(x+5)}{(x+1)(x+3)}$ days. Hence, the answer is (A).