CAT (QA) PYQs

A man leaves his home and walks at a speed of $12$ km per hour, reaching the railway station $10$ minutes after the train had departed. If instead he had walked at a speed of $15$ km per hour, he would have reached the station $10$ minutes before the train's departure. The distance (in km) from his home to the railway station is

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

Two trains cross each other in $14$ seconds when running in opposite directions along parallel tracks. The faster train is $160$ m long and crosses a lamp post in $12$ seconds. If the speed of the other train is $6$ km/hr less than the faster one, its length, in m, is