Question

Three friends A, B and C decide to run around a circular track. They start at the same time and run in the same direction. A is the quickest and when A finishes a lap, it is seen that C is as much behind B as B is behind A. When A completes 3 laps, C is the exact same position on the circular track as B was when A finished 1 lap. Find the ratio of the speeds of A, B and C?
5 : 4 : 2
4 : 3 : 2
5 : 4 : 3
3 : 2 : 1

Answer 1

Answer:

5 : 4 : 3

Step-by-step explanation:

Let say Circular Lap was   x km

B was a km behind A when A completed lap

so Position of B = x - a  km

position of C = x -a - a = x - 2a km

let say t was time taken  

Speed of A , B & C respectively =  x/t   , (x-a)/t  , (x-2a)/t

When A completed 3 laps distance covered by a = 3x

time take = 3x/(x/t) = 3t

B completed the distance =  3x - 3a  km

C completed the Distance = 3x - 6a  km

3x - 6a  has same position as  x-a  

either 3x - 6a = x-a  (did not complete even single lap)

or 3x-6a = x + x - a  (completed one lap)

=> x = 5a/2    or x = 5a

Ratio of Speed of A, B , C are (5a/2)/t  : (5a/2 - a)/t  : (5a/2 - 2a)/t  ,

5 : 3 : 1  ( option not given)

or

Ratio of Speed of A, B , C are (5a)/t  : (5a - a)/t  : (5a - 2a)/t  ,

5 : 4 : 3

5 : 4 : 3 is the option given so this is the right answer