Question

the ratio of time taken by a cyclist to go around the outer and inner circumference of a circular path is 20:19. if the path is 15m. wide. calculate the length of the diameter of the inner circle​

Answer 1

Answer:

570 m

Step-by-step explanation: Assuming that the speed of the cyclist remains same in each case. Let that the speed be 'S'.  

        Using, distance = speed * time

       (circumference) = S * time

For the small circle(let radius be r₁).

        distance₁ = S * t₁

                2πr₁ = S * t₁     ...(1)

For the bigger circle(let radius be r₂)

       distance₂ = S * t₂

                2πr₂ = S * t₂    ...(2)

Dividing (2) by (1):  [big circle to small]

  2πr₂ : 2πr₁ = t₂ : t₁

      r₂ : r₁ = 20 : 19     [given, t₂:t₁=20:19]

Let r₂ be 20x  and  r₁ by 19x.

 Given,  path is 15m wide

So,    r₂ - r₁ = 15

  20x - 19x = 15

               x = 15

∴ Radius of inner circle = 19x = 19(15)

                          = 285m

∴ Diameter of inner circle = 2 * radius

                          = 570 m

Answer 2

Answer :

• 570 m

Solution :

$\longrightarrow$ Let the radius of outer and inner circle be $R$ and $r$ Respectively,

According to the given condition,

• $\sf \frac{2πR}{2πr} = \frac{20}{19}$

• $\sf \frac{R}{r} = \frac{20}{19}$

• $\sf R = \frac{20r}{19}$

$\longrightarrow$ Width of the path is given as 15m,

$\longrightarrow$ Which is equal to R – r = 15 m

So,

• $\sf \frac{20r}{19} - r = 15m$

• $\sf \frac{20r - 19r }{19} = 15$

• $\sf \frac{r}{19} = 15$

• $\sf r = 19 × 15$

r = 285 m

And R = $\sf \frac{20r }{19}$

• R = $\sf \frac{20 (285)}{19}$

• R = $\sf \frac{20 \cancel{(285)}^{\: \: 15× \cancel{19}}}{\cancel{19}}$

• R = 20 × 15

R = 300 m

Finally,

$\longrightarrow$ Diameter of Inner circle = d = 2r

(diameter = 2 × radius)

$\longrightarrow$ 2r = 2(285) = 570 m

Hence,

Diameter of Inner circle = 570 m

I hope it helps you ❤️✔️