Question

The ratio of the outer and inner circumferences of a circular path is $23:22$, If the path is $5m$ wide, the radius of the inner circle is:

• A. $55m$
• B. $110m$
• C. $220m$
• D. $230m$

Answer 1

Answer: (B)

$110m$

Let R and r be the outer and inner radii of the circular path.

Given that,

$\frac{2\pi R}{2\pi r}=\frac{23}{22}$

$=>\frac{R}{r}=\frac{23}{22}$

Let $R=23x$ and $r=22x$

It is given that the width of the path is $5$m wide

$\therefore R-r=5$m

$=>23x-22x=5$

$=>x=5$

$\therefore$ the inner radius of the circle is

$=22\times 5$

$=110$m