Discussion Forum

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 :

Answer:

Explanation:

$2$ kmph $=\left(2\times\frac{5}{18}\right)$ m/sec $=\frac{5}{9}$ m/sec and $4$ kmph $=\frac{10}{9}$ m/sec.

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

Then, $\frac{x}{\left(y-\frac{5}{9}\right)}=9$ and $\frac{x}{\left(y-\frac{10}{9}\right)}=10$.

$\therefore 9y-5=x$ and $10(9y-10)=9x$ $\Rightarrow 9y-x=5$ and $90y-9x=100$.

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

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