Two persons are walking in the same direction at rates 3 km/hr and 6 km/hr. A train comes running from behind and passes them in 9 and 10 seconds. The speed of the train is

Let the speed of train = S km/hr

Let the length of train = x meters

When a train crosses a man, it travels its own distance.

According to question,

Distance = Speed$$ \times $$Time

x = (S - 3)$$ \times \frac{5}{18} \times 9$$      (1)

Also,

x = (S - 6)$$ \times \frac{5}{18} \times 10$$      (2)

From equation (1) and (2)

(S - 3)$$ \times \frac{5}{18} \times 9$$ = (S - 6)$$ \times \frac{5}{18} \times 10$$

(S - 3)$$ \times $$9 = (S - 6)$$ \times $$10

9S - 27 = 10S - 60

10S - 9S = 60 - 27

S = 33 km/hr