1.121 A wheel has a rubber tire with an outer diameter of 25 inches. When the radius is reduced by $\frac{1}{4}$ inch, the number of revolutions in one mile will
(A) increase by about $2 \%$.
(B) increase by about $1 \%$.
(C) increase by about $20 \%$.
(D) increase by $\frac{1}{2} \%$.
(E) remain unchanged.
(7th American High School Mathematics Examination, 1956)
[Solution] Let the number of rotations per mile for the two tires be $n_{1}, n_{2}$, then the increase rate of the number of rotations after the radius decreases is
$$
\frac{n_{2}-n_{1}}{n_{1}}=\frac{\frac{1}{2 \pi\left(r-\frac{1}{4}\right)}-\frac{1}{2 \pi r}}{\frac{1}{2 \pi r}}=\frac{\frac{1}{4}}{r-\frac{1}{4}}=\frac{1}{49} \approx 2 \% .
$$

Therefore, the answer is $(A)$.