CAT (QA) PYQs

A train travelled at one-thirds of its usual speed, and hence reached the destination $30$ minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for $5$ minutes but then stopped for $4$ minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to

A train travelled a certain distance at a uniform speed. Had the speed been $6$ km per hour more, it would have needed $4$ hours less. Had the speed been $6$ km per hour less, it would have needed $6$ hours more. The distance, in km, travelled by the train is

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