Time, Speed and Distance Question 11 - CAT 2020
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:
Step-by-Step Explanation
Let the train's speed be V km/hr. When a train passes a walking person, the distance covered is equal to the length of the train (L). Since the train length L is constant in both cases, the relative speeds are inversely proportional to the crossing times:
Relative Speed Ratio = (V − 2)/(V − 4) = 100/90 = 10/9
9(V − 2) = 10(V − 4)
9V − 18 = 10V − 40
V = 22 km/hr
To cross a stationary post, the train must cover its own length L at its actual speed V (22 km/hr).
We know that at a relative speed of V − 2 = 20 km/hr, it takes the train 90 seconds to cover distance L. Since time is inversely proportional to speed for a constant distance:
Time to cross post = 90 seconds × 20/22
= 1800/22 ≈ 81.81 seconds ≈ 82 seconds
Correct Option: B
💡 FundaMakers Tip:
You can bypass converting units to meters and calculating the train length L entirely! By using the inverse relationship between speed and time (Time₁ × Speed₁ = Time₂ × Speed₂), you can find the train's speed and scale the final crossing time using a simple ratio, keeping your math clean.