Question

Two trains pass each other on parallel lines Each train is $100$ m long. When they are going in the same direction the faster one takes $60$ seconds to pass the other completely. If they are going in opposite directions they pass each other completely in $10$ seconds. Find the speed of the slower train in km/hr

• A. $30$ km/hr
• B. $42$ km/hr
• C. $48$ km/hr
• D. $60$ km/hr

Answer 1

The correct option is A $30$ km/hr

Let the speed of the faster train be $x$ km/hr and that of the slower train be $y$ km/hr.
Relative speed when both move in same direction $=(x-y)$ km/hr
Relative speed when both move in opposite direction $=(x+y)$ km/hr Total distance travelled $=$ Sum of lengths of both the trains $=200$ m
Given, $\frac{200}{(x-y)\times \frac{5}{18}}=60$ and $\frac{200}{(x-y)\times \frac{5}{18}}=10$

$\Rightarrow \frac{3600}{5(x-y)}=60$ and $\frac{3600}{5(x+y)}=10$
$\Rightarrow x-y=\frac{3600}{300}=12$ ....(i)
and $x+y=\frac{3600}{50}=72$ ....(ii)
Adding eqn (i) and eqn (ii), we get

$2x=84$

$\Rightarrow x=42$ km/hr
$\therefore$ From (i), $y=30$ km/hr