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 $30\text{km/hr}$. 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 direction is

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

Answer 1

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

Let $v_1$ and $v_2$ be the velocity of passenger train and freight train respectively.
Let $t_1$ and $t_2$ be the time taken by the passenger train to completely cross the freight train when they are moving in the same direction and when they are moving in the opposite direction respectively.
When trains are moving in same direction releative speed = $|v_1-v_2|$ and in opposite direction relative speed = $|v_1+v_2|$
Hence, ratio of time when trains move in same direction with time and when trains move in opposite direction is
$\frac{t_1}{t_2}=\frac{\left(\frac{l_1+l_2}{|v_1-v_2|}\right)}{\left(\frac{l_1+l_2}{|v_1+v_2|}\right)}=\left|\frac{v_1+v_2}{v_1-v_2}\right|$
where, $l_1+l_2$ = sum of length of trains
which is same as distance covered by trains to cross each other
So, $\frac{t_1}{t_2}=\frac{80+30}{80-30}=\frac{110}{50}=\frac{11}{5}$