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?

- 60
- 36
- 24
- 48

60 Minutes

Try upto 40 hours for free

Learn from the best!

Online Batches Available Now!

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 * t^{2} = 54 * 24 * ab

=> t^{2} = 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.

Choice A is the correct answer.

CAT 2021

Enroll at

44,000/-

Online Classroom Batches Starting Now!

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com