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

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?

1. 36 km/hr
2. 45 km/hr
3. 67.5 km/hr
4. 18 km/hr

Explanatory Answer

Method of solving this CAT Question from Time Speed Distance: Find the time taken for Cars B and C to cross each other and then find the speed of Car A to cover the distance within that time.

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.

Hence, the answer is 67.5kmph.

Choice C is the correct answer.