The question is from the topic Time Speed and Distance. It involves the idea of relative speed. CAT exam is known to test on multiple ideas in the same question, so you should be ready to face them. 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 8: Car A trails car B by 50 meters. Car B travels at 45km/hr. Car C travels from the opposite direction at 54km/hr. Car C is at a distance of 220 meters from Car B. If car A decides to overtake Car B before cars B and C cross each other, what is the minimum speed at which car A must travel?

- 36 km/hr
- 45 km/hr
- 67.5 km/hr
- 18 km/hr

67.5 km/hr

Valid until 16th May

Online Batches Available Now!

To begin with, let us ignore car A. Car B and car C travel in opposite directions.

Their relative speed = Sum of the two speeds = 45 + 54 kmph = 99kmph.

= 99 * \\frac{5}{18}\\)m/s = \\frac{55}{2}\\)m/s = 27.5m/s

The relative distance = 220m. So, time they will take to cross each other = \\frac{220}{27.5}\\) = 8 seconds

Now, car A has to overtake car B within 8 seconds. The relative distance = 50m

=> Relative speed should be at least \\frac{50}{8}\\)m/s = 6.25 m/s.

=>6.25 * \\frac{18}{5}\\)kmph = 22.5 kmph

The question is **" If car A decides to overtake Car B before cars B and C cross each other, what is the minimum speed at which car A must travel? "**

Car B travels at 45kmph, so car A should travel at at least 45 + 22.5 = 67.5kmph.

Choice C 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