Question

A passenger train of length $60\text{m}$ travels at a speed of $80\text{km/hr}$. Another freight train of length $120\text{m}$ travels at a speed of $30\text{km/h}$. The ratio of times taken by the passenger train to completely cross the freight train when :
(i)they are moving in the same direction, and
(ii) in the opposite directions is:

• A. $\frac{11}{5}$
• B. $\frac{5}{2}$
• C. $\frac{3}{2}$
• D. $\frac{25}{11}$

Answer 1

The correct option is A $\frac{11}{5}$

Given:
$l_p=60\text{m}=0.06\text{km};V_p=80\text{km/h}$
$l_f=120\text{m}=0.12\text{km};V_f=30\text{km/h}$

$\left(i\right)$ When they are moving in the same direction, the time taken to completely cross the freight train by the passenger train be

$t_1=\frac{d_{total}}{V_{relative}}$

$=\frac{0.06+0.12}{80-30}=\frac{0.18}{50}....\left(1\right)$

$\left(ii\right)$ When they are moving in the opposite direction, the time taken to completely cross the freight train by the passenger train be

$t_2=\frac{d_{total}}{V_{relative}^{\prime }}$

$=\frac{0.18}{80+30}=\frac{0.18}{110}....\left(2\right)$

Using equations $\left(1\right)$ and $\left(2\right)$,

$\frac{t_1}{t_2}=\frac{110}{50}=\frac{11}{5}$

Hence, $\left(A\right)$ is the correct answer.