cat 2023 Question 11

Question

Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is

Accepted Answer

It is given that the speed of Ravi is 40 kmph, which is equal to $ \frac{100}{9} $ m/s. It is also known that the speed of Ashok is 50 kmph, which is equal to $ \frac{125}{9} $ m/s.

It is known that the distance between Ravi and Ashok is 225 meters, and the relative speed of Ravi and Ashok is $ \frac{125}{9} + \frac{100}{9} = 25 $ m/s

Hence, they will meet each other in $ \frac{225}{25} = 9 $ seconds. The distance traveled by Ravi in these 9 seconds is $ \frac{100}{9} imes 9 = 100 $ meters.

Since Vijay was already 54 meters behind Ravi when they were starting, Vijay must travel (100+54) = 154 meters in these 9 seconds.

Hence, the speed of Vijay is $ \frac{154}{9} $ m/s, which is equal to $ \frac{154}{9} imes \frac{18}{5} = \frac{308}{5} = 61.6 $ kmph.

The correct option is D

Question 11.

Question Explanation