Question

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

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

Answer 1

Answer: (A)

33 km/hr

Let the speed of the train be x km/hr. & its length $=y$ km.

Now A train covers its own length when it crosses a person.

So the distance covered by the train in each case $=y$ km.

In the first case, the relative speed of the first person and the train$=(x-3)$km/hr. and

in the second case, the relative speed of the second person and the train$=(x-6$)km/hr.

So, in the first case, the time taken=$\frac{y}{x-3}$hrs. and

in the second case, the time taken=$\frac{y}{x-6}$hrs.

$\therefore$ By the given condition,

in the first case, $\frac{y}{x-3}=9$ Or $y=9x-27$.........(i)

and

in the second case, $\frac{y}{x-6}=9$ Or $y=10x-60$.........(ii).

Comparing (i) & (ii),

$9x-27=10x-60$

Or $x=33km/hr$.

So the speed of the train = $33$km/hr.