Question

A man walks around two circular fields, field one and field two in 11 sec and 33 sec respectively. If the ratio of speed while walking in field one and field two is  2 : 1 and the radius of field one is 14 m, then find the radius of field two. 
1. 40 m
2. 21 m
3. 15 m
4. 30 m
5. 25 m

Answer 1

Correct Answer - Option 2 : 21 m

Given : 

Time taken to walk around field 1 = 11 s

Time taken to walk around field 2 = 33 s

Formula used :

Speed = Distance/ Time 

Calculations :

Let the radius of field 1 and field 2 be r₁ and r₂ respectively.

And the speeds while traveling in field 1 and field 2 are 2x and x respectively.

Distance traveled = Perimeter of the fields 

⇒ Distance 1/Distance 2 = (speed× time)₁ / (speed× time)₂

⇒ Distance 1/Distance 2 = (2x × 11)/(x × 33)

⇒ 2/3 = r₁/r₂

⇒ r₂ = 3/2 × r₁

⇒ r₂ = 3/2 × 14

⇒ r₂ = 21 m

∴ The radius of field two is 21 m.