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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(in metres) is:

1. $45$
2. $54$
3. $50$
4. $72$

Let length of train be x and speed of the train be y

Case 1 – Person A  → S = $2*\frac{5}{18}m/sec$      t = 9 sec

Case 2 – Person B  → S = $4*\frac{5}{18}m/sec$      t = 10 sec

Dist in Case 1 →  $\frac{x}{y-\frac{10}{18}}=9$   →  x = 9y – 5   -----(1)

Dist in Case 2 →  $\frac{x}{y-\frac{10}{9}}=10$   →  x = 10y – $\frac{100}{9}$   -----(2)

On solving (1) and (2), we will get x = 50 and y = $\frac{55}{9}$

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