CAT 2018 Slot 1 QA Question 8: Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P o

Question

Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P o

Accepted Answer

Let $AP = d$. Then $BP = 3d$.
Let the speed of car 1 be v. Then the speed of car 2 is $\dfrac{v}{2}$.
Time taken by car 1 to reach P $=\dfrac{d}{v}$
Time taken by car 2 to reach P $=\dfrac{3d}{\dfrac{v}{2}} = \dfrac{6d}{v}$
The difference is 1 hour.
$\dfrac{6d}{v} - \dfrac{d}{v} = 1$
$\dfrac{5d}{v}