CAT 2020 Question Paper | Quants Slot 1

CAT Previous Year Paper | CAT Quants Questions | Question 14

Speed time distance is one of the most commonly tested topics in CAT exam. Questions from speed time distance have appeared consistently in the CAT exam for the last several years. This topic is very interesting as it is relatable in real-life scenarios. This Question is about relative speed. It discusses a train crossing two persons. We need to find the time taken by train to cover an electric post.

Question 14 : Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

  1. 87
  2. 82
  3. 78
  4. 75

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Explanatory Answer

Two person to be A and B
A = 2km/hr and B = 4 km/hr
Speed of the train = t km/hr
Given, Train crosses A in 90 seconds (Length of the train is the distance)
t – 2 in 90 seconds and t – 4 in 100 seconds
Ratio of speed is opposite to time
(t – 2) 90 = (t - 4) 100
Solving t = 22km/hr
For A, Speed = t – 2 = 20 km/hr in 90 seconds
So travelling at 22 km/hr ----> \\frac{90 × 20}{22}) ≅ 82


The answer is, "82"

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