1956 AMC 12 Problem 45

Question

A wheel with a rubber tire has an outside diameter of

25

in. When the radius has been decreased a quarter of an inch, the number of revolutions in one mile will:

be increased about

2\%

be increased about

1\%

be increased about

20\%

be increased

\dfrac12\%

remain the same

For a fixed distance, the revolution count is inversely proportional to the wheel’s radius

Compare the original radius

12.5

with the new radius

12.25

The original radius is

12.5

inches and the new radius is

12.25

inches. For a fixed distance, the number of revolutions varies inversely with radius, so the relative increase is

\begin{aligned} \frac{12.5}{12.25}-1 &=\frac{50}{49}-1\\ &=\frac1{49}\\ &\approx2.04\%. \end{aligned}

This is about

2\%.

Thus, the correct answer is A.

Problem 45 in other years