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
Answers
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