Question

Two trains $A$ and $B$ travel in two parallel rail tracks in opposite direction with speed $v_1$ and $v_2$, respectively. They take $4s$ to pass each other at this speed. If the speed of train $A$ is increased by $50\%$, then they take 3 s to pass each other. The ratio of $v_1/v_2$ is

• A. 0 : 5
• B. 1 : 5
• C. 2 : 1
• D. 2 : 5

Answer 1

Answer: (C)

Relative velocity of trains $=v_1+v_2$
Let distance between them is $s$.
(i) First they take $4s$ to cross
$s=\left(v_1+v_2\right)4$ ...(i)
(ii) Second they take $3s$ to cross, when speed of train A is increased by $50\%$.
Now, relative velocity
$=\left(v_1+\frac{50}{100}{v}_1\right)+v_2$
$=\left(\frac{3}{2}{v}_1+v_2\right)$
$\therefore s={\left(\frac{3}{2}{v}_1+v_2\right)}^3$ ...(ii)
From Eqs. (i) and (ii), we get
$\left(v_1+v_2\right)4=\left(\frac{3}{2}{v}_1+v_2\right)3$
$\Rightarrow v_2=\frac{v_1}{2}$
$\Rightarrow \frac{v_1}{v_2}=\frac{2}{1}$