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.