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 $4\, s$ 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 $4 s$ to cross
$s=\left(v_{1}+v_{2}\right) 4$ ...(i)
(ii) Second they take $3\, s$ 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
$\left(v_{1}+v_{2}\right) 4=\left(\frac{3}{2} v_{1}+v_{2}\right) 3$
$\Rightarrow v_{2}=\frac{v_{1}}{2}$
$\Rightarrow \frac{v_{1}}{v_{2}}=\frac{2}{1}$