CAT (QA) PYQs

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

Leaving home at the same time, Amal reaches the office at $10:15 am$ if he travels at $8 km/hr$, and at $9:40 am$ if he travels at $15 km/hr$. Leaving home at 9:10, at what speed, in $km/hr,$ must be travel so as to reach office exactly at $10 am?$

Vimla starts for office every day at $9$ am and reaches exactly on time if she drives at her usual speed of $40 \mathrm{~km} / \mathrm{hr}$. She is late by $6$ minutes if she drives at $35 \mathrm{~km} / \mathrm{hr}$. One day, she covers two-thirds of her distance to office in onethirds of her usual time to reach office, and then stops for $8$ minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is