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?
Answer & explanation
Correct answer: option 3
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.