Question

A train overtakes two persons walking along a railway track. The first one walks at $4.5$ km/hr. The other one walks at $5.4$ km/hr. The train needs $8.4$ and $8.5$ seconds, respectively, to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

• A. $81$ km/hr
• B. $82$ km/hr
• C. $83$ km/hr
• D. $84$ km/hr

Answer 1

The correct option is A $81$ km/hr

Let the speed of the train be $x$ km/hr
Relative speed of train w.r.t first person $=(x-4.5)$ km/hr $=(x-4.5)\times$ $\frac{5}{18}$ m/s
Relative speed of train w.r.t second person $=(x-5.4)$ km/hr $=(x-5.4)\times$ $\frac{5}{18}$ m/s
Length of the train $=$ $(x-4.5)\times \frac{5}{18}\times 8.4=(x-5.4)\times \frac{5}{18}\times 8.5$
$\Rightarrow 8.4x-37.8=8.5x-45.9$

$\Rightarrow 0.1x=45.9-37.8=8.1$

$\Rightarrow x=81$ km/hr