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Previous Year Question (PYQs)



A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:





Solution

Let train 
speed $= V$ kmph, 
length $= L$ metres 

Equation 1 (passes 2 kmph walker in 9s): $$L = (V-2) \times \frac{5}{18} \times 9$$ 
 Equation 2 (passes 4 kmph walker in 10s): $$L = (V-4) \times \frac{5}{18} \times 10$$ Equating both: $$45(V-2) = 50(V-4)$$ $$45V - 90 = 50V - 200 \Rightarrow V = 22 \text{ kmph}$$ Length: $$L = (22-2) \times \frac{5}{2} = \boxed{50 \text{ metres}}$$


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