The given question consists of a set of statements. Find out whether the data provided in the statements are sufficient to answer the question and mark the option:

What is the speed of the passenger train?
I. The train crosses a signal pole in 27 seconds.
II. The train crosses a platform of equal length in 54 seconds.
III. Length of the train is 495 metres.

I and II only

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II and III only

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I and III only

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III and either I or II only

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Any two of the three

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Solution

The correct option is D
III and either I or II only

Let the speed of the train be 'x' m/sec.

Time taken to cross a signal pole $= \frac{L e n g t h o f t r a i n}{S p e e d o f t r a i n}$

Time taken to cross a platform $= \frac{(L e n g t h o f t r a i n + L e n g t h o f p l a t f o r m)}{S p e e d o f t h e t r a i n}$

Length of train = 495 m

$I a n d I I I g i v e, 27 = \frac{495}{x} \Rightarrow x = \frac{495}{27} m / s = \frac{55}{3} m / s . I I a n d I I I g i v e, 54 = \frac{2 \times 495}{x} \Rightarrow x = \frac{990}{54} m / s = \frac{55}{3} m / s .$

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