Correct Answer: 81 km/hr
Explanation:
Step 1: Convert walking speeds to m/s
Step 2: Let the length of the train be L meters
We know:
Time = Distance / Relative Speed So, L / (Train Speed - Person Speed) = Time
Use the first case (Person walking at 1.25 m/s):
L / (V - 1.25) = 8.4 → (1)
Use the second case (Person walking at 1.5 m/s):
L / (V - 1.5) = 8.5 → (2)
Step 3: Solve the two equations
From (1): L = 8.4 × (V - 1.25)
From (2): L = 8.5 × (V - 1.5)
Equating both expressions for L:
8.4(V - 1.25) = 8.5(V - 1.5)
Expand both sides:
8.4V - 10.5 = 8.5V - 12.75
Bring all terms to one side:
8.5V - 8.4V = 12.75 - 10.5 0.1V = 2.25 ⇒ V = 2.25 / 0.1 = 22.5 m/s
Step 4: Convert train speed to km/h
22.5 m/s = 22.5 × 18 / 5 = 81 km/h
Answer: The speed of the train is 81 km/h.
This type of problem uses the concept of relative speed and distance = speed × time. It’s a common question in aptitude tests, and mastering it builds speed and accuracy for competitive exams.
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