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

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55 m

110 m

220 m

230 m

answer is B.

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Detailed Solution

It is given the ratio of the outer and inner circumferences of a circular path is

23 : 22

.
A draft picture has been drawn below.
Question Image

Let R and r be the outer and inner radii of the circular path.
According to the condition,

\frac{2 πR}{2 πr} = \frac{23}{22}

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

Now let

R = 23 x

and

r = 22 x

.
The width of the path is

5

m wide

∴ R - r = 5

\Rightarrow 23 x - 22 x = 5

\Rightarrow x = 5

∴

The inner radius of the circle is

= 22 \times 5

= 110

m.
Hence, option 2 is correct.

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