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
(a)55 m
(b)110 m
(c)220 m
(d)230 m

Answer 1

Answer:

The Diameter of inner circle is  220 m.

Among the given options option (c) 220 m is the correct answer.

Step-by-step explanation:

Let outer and inner circumference of the circular path be C1 & C2 and the outer radius of the circular path be ‘R’ and inner radius be ‘r’

Given :  

Ratio of  the outer and inner Perimeters of the circular path,C1 : C2  = 23 : 22

Width of circular path, (R - r) = 5 …….(1)

Circumference of a circle = 2πr

C1 : C2 = 23 : 22

2πR : 2πr = 23 : 22

R : r = 23 : 22

22R = 23r

R = 23r/22

On putting the value of R in eq 1

R - r = 5

23r/22 - r = 5

(23r - 22r)/22 = 5  

r = 22 × 5  

r = 110 m

Radius of a inner circle, r = 110 m

Diameter of inner circle , d = 2 × r  

d = 2 × 110

d = 220 m

Diameter of inner circle = 220 m

Hence, the Diameter of inner circle is  220 m.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer

Let R = 23x and r = 22x

It is given that the width of the path is 5 m wide

here, R – r = 5 m

• 23x – 22x = 5 m

• x = 5 m

The external diameter of the circular road = 2 × 23 × 5 m = 230 m

The diameter of the circular road = 2 × 22 × 5 m = 220 m

Answer=220m