$3 \cdot 16$ If the marked price of an item is $p$ percent higher than the cost, and then, to recover the cost, the discount on the selling price cannot exceed $d$, then the value of $d$ is
(A) $\frac{1}{1+p}$.
(B) $\frac{1}{1-p}$.
(C) $\frac{p}{1+p}$.
(D) $\frac{p}{p-1}$.
(E) $\frac{1-p}{1+p}$.
(4th American High School Mathematics Examination, 1953)
[Solution] Let the cost of the item be $I$, and the selling price be $S$. According to the problem, we have $S=I(1+p)$, and also $S(1-d)=I$. Eliminating $S, I$ yields $(1+p)(1-d)=1$, thus $d=\frac{p}{1+p}$. Therefore, the answer is $(C)$.