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

Solution

## The correct option is A I and II onlyLet 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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