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A $300$ metre long metro train crosses a platform in a metro station in $39$ seconds while it crosses a lamp post in $18$ seconds. What is the length of the platform?

1. $250$ metre
2. $350$ metre
3. $520$ metre
4. $300$ metre

Lets say length of platform is $\text{L metre}.$

We know that $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

$S_{\text{train}} = \dfrac{300}{18}\;\text{metre/sec} = \dfrac{50}{3}\;\text{metre/sec}$

$S_{\text{train}} = \dfrac{300 + L}{39}\;\text{metre/sec}$

$\implies \dfrac{50}{3} = \dfrac{300 + L}{39}$

$\implies 300 + L = 50 \times 13 = 650$

$\implies L = 350\;\text{metre}.$

So, the correct answer is $(B).$
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