Question

Two persons are walking in the same direction at rates $3$ km/hr and $6$ km/hr. A train comes running from behind and passes them in $9$ and $10$ seconds. What is the speed of the train?

• A. $22$ km/hr
• B. $40$ km/hr
• C. $33$ km/hr
• D. $35$ km/hr

Answer 1

Answer: (C)

$33$ km/hr

Let us Assume the velocity of the Train be $V$ and the time in which the train passes the $2$ persons be $t_1,t_2$

and Now converting seconds to hours, we get $t_1=\frac{9}{3600}hr$

and $t_2=\frac{10}{3600}hr$

Also, velocity of Train with respect to the Persons are $(V-3)and(V-6)$ respectively.

Now we know that Length of the Train is Constant and $Velocity=\frac{distance}{time}$

$\Rightarrow (V-3)\frac{9}{3600}=(V-6)\frac{10}{3600}$

Solving it we will get

$\Rightarrow 9V-27=10V-60$

$\Rightarrow V=33km/hr$

Therefore Answer is $\left(C\right)$