Management Aptitude Test 2016 Paper

(d) Let the speed of the train be x m/s.
When train overtakes first person, then
Relative speed
= $\left(\mathit{x}-4.5\times \frac{5}{18}\right)$ m/s
= $\left(\mathit{x}-\frac{5}{4}\right)$ m/s
Time = 8.4 s [given]
∴ Distance = $\left(\mathit{x}-\frac{5}{4}\right)$ × 8.4
= 8.4x - $\frac{5\times 8.4}{4}$ = 8 .4 x - 5 × 2.1
= 8.4 x - 10.5 .........(i)
When train overtakes second person, then
Relative speed = $\left(\mathit{x}-5.4\times \frac{5}{18}\right)$ m/s
= $\mathit{x}-\frac{3}{2}$
∵ Time = 8.5 s [given]
∴ Distance = $\left(\mathit{x}-\frac{3}{2}\right)$8.5
= 8.5x - $\frac{3\times 8.5}{2}$
= 8.5x - 12.75 ........(ii)
From Eqs (i) and (ii), we get
8.4x - 10.5 = 8.5x - 12.75
⇒ 0.1x = 2.25
⇒ x = $\frac{2.25}{0.1}$ = 22.5 m/s
= 22.5 × $\frac{18}{5}$ km/h = 81 km/h