Question

The diameters of two wheels are $10$ in. and $14$ in. The smaller makes $50$ more revolutions than the larger in going a certain distance. This distance, in inches, is

• A. $3500$
• B. $1750$
• C. $1750$ $\pi$
• D. $3500$ $\pi$
• E. none of these

Answer 1

Answer: (C)

$1750$ $\pi$

The radius of two wheels are $5$ inch and $7$ inch
The distance traveled by smaller in one revolution is $2\pi \times 5=10\pi$
The distance traveled by larger in one revolution is $2\pi \times 7=14\pi$
Given that for $x$ distance , if larger takes $n$ revolutions, then smaller takes $n+50$ revolutions
Therefore we get $2\pi \times 7\times n=2\pi \times 5\times (n+50)$ $\Rightarrow n=125$
Therefore, $x=2\pi \times 7\times 125=1750\pi$