The ratio of the outer and the inner circumference of a circular path is 5 : 4. If path is 50 metres wide, then what is the radius of the inner circle?

200 metres

 Perimeter of the circle = 2 πr

Let the radius of outer and inner circle be R and r m, then

Circumference of outer circle = 2πR

Circumference of inner circle = 2πr

According to the question

\(\frac{2 πR}{2 πr}\) = \(\frac{5}{4}\)

⇒ \(\frac{R}{r}\) = \(\frac{5}{4}\)

⇒ R : r = 5x : 4x

Length of path (R – r) = 50 m

5x – 4x = 50

⇒ x = 50

⇒ 4x = 200m.