Management Aptitude Test 2016 Paper

(a) ∵ Speed of first train,
${\mathit{s}}_1$ = 48 km/h = $\frac{40}{3}$ m/s
and speed of second train,
${\mathit{s}}_2$ = 42 km/h = $\frac{35}{3}$ m/s
Let the length of first train be d m.
Then, length of second train = $\frac{\mathit{d}}{2}$ m
∴ Relative speed = ${\mathit{s}}_1$ + ${\mathit{s}}_2$
= $\frac{40}{3}+\frac{35}{3}=\frac{75}{3}$ = 25 m/s
According to the question,
d + $\frac{\mathit{d}}{2}$ = 25 x 12
⇒ $\frac{3\mathit{d}}{2}$ = 25 x 12
⇒ d = $\frac{25\times 12\times 2}{3}$ = 200 m
Again, let length of the platform be l m.
Then, 200 + l = $\frac{40}{3}$ x 45
⇒ 200 + l = 600
⇒ l = 600 - 200 = 400 m