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Question

What is the speed of the train?
I. The train crosses a tree in 13 seconds.
II. The train crosses a platform of length 250 metres in 27 seconds.
III. The train crosses another train running in the same direction in 32 seconds.


A
I and II only
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B
II and III only
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C
I and III only
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D
Any two of the three
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E
None of these
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Solution

The correct option is A I and II only
Let the speed of the train be x metres/sec.
Time taken to cross a tree $$= \dfrac{{Length\ of\ the\ train}}{\text{Speed of the train}}$$
Time taken to cross a platform $$= \dfrac{\text{(Length of the train + Length of the Platform)}}{\text{Speed of the train}}$$
I gives, $$13 = \dfrac{l}{x} \Rightarrow 13 x$$
II gives $$27 = \dfrac{l + 250}{x}$$
$$\Rightarrow \dfrac{13 x + 250}{x} = 27$$
$$\Rightarrow x = \dfrac{125}{7} m/sec.$$
Thus I and II give the speed of the train.
$$\therefore$$ The correct answer is (A).

Logical Reasoning

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