Question

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

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

Answer 1

The correct option is C $220m$

Given

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

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

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

$\therefore R-r=5$

$23x-22x=5$

$x=5$

$\Rightarrow r=22\times 5=110$

Diameter of inner circle $=2r$

$=2\times 110$

$=220m$