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:

45 m

50 m

54 m

72 m

Explanation:

2 kmph =$ \left(2 \times\dfrac{5}{18} \right) $m/sec =$ \dfrac{5}{9} $m/sec.

4 kmph =$ \left(4 \times\dfrac{5}{18} \right) $m/sec =$ \dfrac{10}{9} $m/sec.

Let the length of the train be $ x $ metres and its speed by $ y $ m/sec.

Then,

$ x $

= 9 and

$ x $

= 10.

$\therefore 9 y $ - 5 = $ x $ and 10$\left(9 y - 10\right)$ = 9$ x $

$\Rightarrow 9 y $ - $ x $ = 5 and 90$ y $ - 9$ x $ = 100.

On solving, we get: $ x $ = 50.

$\therefore$ Length of the train is 50 m.