CAT 2018 Question Paper | Quants Slot 1

CAT Questions

Here's a problem involving cars: you guessed it right, the concept is Time, Speed and Distance, which is a major topic in the CAT Syllabus. Solve this not-so-difficult question and check out CAT Previous Year Paper for more such ones. If you find such problems tough and unable to solve, enroll yourself to the Online Classes for CAT offered by 2IIM.

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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Video Explanation

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Explanatory Answer

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

Let us take the distance AP = x and BP = 3x
It’s also given that Speed_Car-2 = \\frac{1}{2}) Speed_Car-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 T_Car-1 = \\frac{x}{S}) T_Car-2 = \\frac{3𝑥}{\frac{S}{2}}) = \\frac{6x}{S})
T_Car-1 = t T_Car-2 = 6t
We know, T_Car-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.