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A train approaches a tunnel XY. There is a dog located inside the tunnel at a point that is 3/8 of the distance XY measured from the entrance X. When the train whistles the dog gets scared and runs. If the dog moves towards the entrance of tunnel X, the train catches the dog exactly at the entrance of the tunnel. If the dog moves to exit Y, the train catches the dog at exactly the exit. Find the ratio of the speed of dog and train.

A train approaches a tunnel XY. There is a dog located inside the tunnel at a point that is 3/8 of the distance XY measured from the entrance X. When the train whistles the dog gets scared and runs. If the dog moves towards the entrance of tunnel X, the train catches the dog exactly at the entrance of the tunnel. If the dog moves to exit Y, the train catches the dog at exactly the exit. Find the ratio of the speed of dog and train. Correct Answer 1 : 4

Calculation:

Let the length of the tunnel be x

The distance of the train and entrance X be y.

Let the speeds of the train and dog be t and d respectively.

Hence, when the dog runs 3x/8, the train covers y.

⇒ (3x/8)/d = y/t      ----(i)

When the dog runs 5x/8 to the other end, the train covers x + y

⇒ (5x/8)/d = (x + y)/t      ----(ii)

∴ taking ratio of (ii) to (i)

⇒ 5/3 = (x + y)/y

⇒ 5y = 3x + 3y

⇒ 2y = 3x       ----(iii)

Substituting (iii) in (i)

(2y/8)/d = y/t

⇒ t = 4d

The ratio of the speed of dog and train is 1 : 4.

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