List of top Quantitative Aptitude Questions on Relative Speed asked in CAT

Rahim drives from city A to station C at \(70\) km/h. Train leaves city B (500 km south of A) at 8:00 am toward C at \(50\) km/h. C is located between S and SW of A with AC at \(30^\circ\) to AB. Rahim must reach C at least 15 minutes before train. Latest time to leave A?

Cities A and B are in different time zones. A is located \(3000 \ \text{km}\) east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.

Departure CityTimeArrival CityTime
B8:00 amA4:00 pm
A3:00 pmB8:00 pm

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at \(50 \ \text{km/h}\).

Arun, Barun, and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40, and 60 km/h respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9:00 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B, and comes back to A at the same speed. 

Train X departs from station A at 11 a.m. for station B, 180 km away. Train Y departs from station B at 11 a.m. for station A. Train X speed = 70 km/h, no stops. Train Y speed = 50 km/h, stops for 15 min at station C, 60 km from B. Ignoring train lengths, find the distance from A to meeting point.
Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom's steps. Shyama gets to the top after taking 25 steps, while Vyom takes 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?