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

Answer: A

Concepts:circumference inverse proportion percent change

Difficulty rating: 1550

Small Hint:

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

Big Hint:

Compare the original radius $12.5$ with the new radius $12.25$

Solution:

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.

1956 AMC 12 Problem 45

Answer: A

Difficulty rating: 1550

Small Hint:

Big Hint:

Solution:

Problem 45 in Other Years