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

CAT Questions | Time and distance | Relative speed

The question is from the topic relative speed. It discusses about a car overtaking a trailer truck. It tests our understanding of relative speed. 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 12: A car of length 4m wants to overtake a trailer truck of length 20m travelling at 36km/hr within 10 seconds. At what speed should the car travel?

  1. 12 m/s
  2. 14.8 m/s
  3. 12.4 m/s
  4. 7.6 m/s

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Explanatory Answer

Method of solving this CAT Question from Time Speed Distance: Understanding relative speed would help.

Given :
car of length = 4 m
length of truck = 20 m
Speed of truck = 36 km/hr

Total distance to be covered by the car 'd' = 20 + 4 = 24 m
Let speed of car be S1 m/s
Speed of truck S2 = 36 km/hr = 10 m/s
Both the car and the truck are travelling in the same direction and we know that to overtake the truck, the speed of the ca should be more than that of the truck.
Hence, relative speed = |S1 - S2|
Time to overtake = 10s

S = \\frac{d}{t}\\)
|S1 - 10| = \\frac{24}{10}\\)
S1 - 10 = 2.4
S1 = 10 + 2.4 = 12.4 m/s

The question is " At what speed should the car travel? "

Hence, the answer is 12.4 m/s

Choice C is the correct answer.


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