Question

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

Options

• 55 m

•  110 m

• 220 m

• 230 m

Answer 1

Let OA = r be the radius of the inner circle and OB = r′ be the radius of the outer circle.

Therefore, circumference of the inner circle `=2pir` and circumference of the outer circle =`2pir`

Here we have to find the diameter of the inner circle.

We have given the ratio of outer and inner perimeters of a circular path.

`∴ (2pi r')/(2pir')=23/22`

Simplifying the above equation we get,

`r'/r=23/22`

`∴ 22 r'=23 r`

`∴ 22r'-23 r=0`             ............(1)

We have also given that the path is 5 meters wide, that is we have given

`r'-r=5`                      ...............(2)

We are asked to find the diameter of the inner circle hence, we will eliminate r′ using equations (1) and (2) for that we will multiply equation (2) by 22.

`22r'-22r=110`    ..............(3) 

Subtracting equation (1) from equation (3) we get, `r=100`

Therefore, radius of the inner circle is 110 meters.

Therefore, diameter of the inner circle =`2xx110=220`meters

Therefore, diameter of the inner circle is`220 meters`