Question

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:

• A. 20 m
• B. 30 m
• C. 40 m
• D. 50 m

Answer 1

The correct option is D 50 m

Let the length of the train be x metres and speed be y $m/s$

Speed of the first person$=2kmph$

$=2\times \frac{5}{18}$

$=\frac{5}{9}m/s$

Speed of the second train $=4kmph$

$=4\times \frac{5}{18}$

$=\frac{10}{9}m/s$

$\frac{x}{y-\frac{5}{9}}=9$

$9y-5=x$

$90y-50=10x$...........................................(1)

$\frac{x}{y-\frac{10}{9}}=10$

$90y-100=9x$...........................................(2)

Substracting $1$ and $2$

$90y-50-90y+100=10x-9x$

$x=50$

So, the length of the train$=50m$