NIFT UG 2019 Question Paper with solutions

Given, length of platform $=50\mathit{m}$
Let the length of train be $\mathit{x}\mathit{m}$
When the train crosses lamp-post, speed $=\frac{\mathit{x}}{10}$
Similarly, when the train crosses the platform, speed
$=\frac{\mathit{x}+50}{14}$
According to the question.
$\frac{\mathit{x}+50}{14}=\frac{\mathit{x}}{10}$
$\Rightarrow 14\mathit{x}=10\mathit{x}+500$
$\Rightarrow 4\mathit{x}=500$
$\therefore \mathit{x}=\frac{500}{4}=125\mathit{m}$
Therefore, speed $=\frac{125}{10}\times \frac{18}{5}$
$=45\mathit{k}\mathit{m}/\mathit{h}$