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:

Answer is C

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 = $\frac{55}{9}$