A man sitting in a train travelling at the rate of $50$ km/hr observes that it takes $9$ sec for a goods train travelling in the opposite direction to pass him. If the goods train is $187.5$ m long, find its speed?

21

km/hr

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23

km/hr

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25

km/hr

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27

km/hr

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Solution

The correct option is C $25$ km/hr
Let the speed of the goods train be $x$ km/hr
Relative speed $= (50 + x)$ km/hr $= (50 + x) \times \frac{5}{18}$ m/s
Therefore, $\frac{187.5}{(50 + x) \times 5 / 18} = 9$
$\Rightarrow \frac{187.5 \times 18}{250 + 5 x} = 9$
$\Rightarrow 250 + 5 x = 187.5 \times 2 = 375$
$\Rightarrow 5 x = 375 - 250 = 125$
$\Rightarrow x = 25$ km/hr

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