CAT Quantitative Aptitude Questions | CAT Time Speed and Distance & Races

The question is from the topic time and distance. It discusses about two friends travelling in opposite directions. It is a classic question involving the concept of speed, distance and time. Time Speed and Distance is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 6: Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?

1. 60
2. 36
3. 24
4. 48

Explanatory Answer

Method of solving this CAT Question from Time Speed Distance: Forming the equations is the key point here.

Let us assume Car A travels at a speed of a and Car B travels at a speed of b.
Further, let us assume that they meet after t minutes.
Distance traveled by car A before meeting car B = a * t. Likewise distance traveled by car B before meeting car A = b * t.
Distance traveled by car A after meeting car B = a * 54. Distance traveled by car B after meeting car A = 24 * b.
Distance traveled by car A after crossing car B = distance traveled by car B before crossing car A (and vice versa).
=> at = 54b ---------- (1)
and bt = 24a -------- (2)
Multiplying equations 1 and 2
we have ab * t² = 54 * 24 * ab
=> t² = 54 * 24
=> t = 36

The question is " How long did B take to cover the entire journey between City Q and City P?"
So, both cars would have traveled 36 minutes prior to crossing each other. Or, B would have taken 36 + 24 = 60 minutes to travel the whole distance.

Hence, the answer is 60 mins.

Choice A is the correct answer.