CAT 2020

Slot 2

QA

Question & Solution

Now car A beats car B by 45km. Let the speed of car A be v(a) and speed of car B be v(b).

$\frac{v\left(a\right)}{v\left(b\right)}=\frac{m}{m-45} .....(1)$

(where '"m" is the entire distance of the race track.)

Moreover 

$\frac{v\left(b\right)}{v\left(c\right)}=\frac{m}{m-50}.......(2)$

and finally 

$\frac{v\left(a\right)}{v\left(c\right)}=\frac{m}{m-90}......(3)$

Multiplying (1) and (2) we get (3)

$\frac{m}{m-90}=\frac{m}{m-45}\left(\frac{m}{m-50}\right)$

Solving we get m=450 which is the length of the entire race track