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Question 17 :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 one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is:[TITA]


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Explanatory Answer

Method of solving this CAT Question from Speed, Time and Distance
Speed, Time and Distance

Let us take the distance AP = x and BP = 3x
It’s also given that SpeedCar-2 = \\frac{1}{2}) SpeedCar-1
S1 = S S2 = \\frac{S}{2} )
Car 2 takes one hour more than Car 1
T2 = t minutes T2 = (t + 60) minutes

We know that Time = \\frac{Distance}{Speed})
So TCar-1 = \\frac{x}{S}) TCar-2 = \\frac{3𝑥}{\frac{S}{2}}) = \\frac{6x}{S})
TCar-1 = t TCar-2 = 6t
We know, TCar-2 takes (t + 60) minutes
6t = t + 60
5t = 60
t = 12 minutes

The question is "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 one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is:"

Hence, the answer is 12 minutes.

Choice C is the correct answer.

 

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