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Two persons are walking beside a railway track at respective | Quantitative Aptitude - CAT TSD

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The question below is from previous year CAT question from CAT 2020 exam comes from CAT Time Speed Distance: 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 

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CAT 2020 - Slot 1 - Quantitative Aptitude - TSD - Question 14 - Two persons are walking beside a railway track at respective

Q.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

Correct Answer: 82

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 —-> 90×20 / 22 ≅ 82

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