A train approaches tunnel A B. Inside the tunnel is a cat located at a point that is of the distance A B measured from the entrance . When the train whistles, the cat runs. If the cat moves to the entrance of tunnel The train catches the cat exactly at the entrance. If the cat moves to the exit The train catches the cat exactly at the exit. The speed of the train is greater than the speed of the cat by what order ?

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3: 1

4:1

5: 1

None of these

answer is B.

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Detailed Solution

Concept- To answer this question, we must first create an abstract mental image, which we then sketch to make the topic more comprehensible. The equations for two situations (depending on the movement of the cat) will then be framed using the formulae, and by doing more calculations, we will approach our solution.
Question Image

Let x be the distance between the train and the tunnel entrance when the train whistles, and let AB be the length of the tunnel.
Let the train and cat go at speeds of T and C, respectively.
Here

is the distance covered by cat and

is the speed of cat while moving towards

which calculates the time taken by cat to reach

. It will be equal to the time taken by train to reach

as the train and cat meet at

and

is the distance covered by the train and

is the speed of the train.
Similarly when the train is moving towards

, it will cover

distance at the speed of

which will calculate time which will be equal to time taken by cat while covering

distance at the speed of