Question: A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is 3/8 of the distance AB measured from the entrance A. When the train whistles the cat runs. If the cat moves to the entrance of the tunnel, A, the train catches the cat exactly at the entrance. If the cat moves to the exit, B, the train catches the cat at exactly the exit. The speed of the train is greater than the speed of the cat by what order?

(A) 3 : 1
(B) 4 : 1
(C) 5 :1
(D) 6 :1
(E) None of these

Correct Answer: (B)
Solutions and Explanation
Approach Solution - 1:

Allow the train to be y distance from point A.
Let the tunnel AB have a length of 8x. The cat is therefore 3 times away from A.
Both of the conditions are now specified in the questions, assuming the same time scenario.
As a result, the ratio of the train's and cat's speeds will be equal to the ratio of their respective distances covered.
=> y/(3x) = (y +8x)/5x
=> y = 12x

Therefore, ratio of the speed = y : 3x = 12x : 3x = 4 : 1

Approach Solution - 2 :

The Cat is 3/8 of the way through the AB tunnel. Let's assume that the tunnel is 80 meters long.
It takes 3 minutes to get to the start if the cat has a rate of 10.
We now know that the train needs the same amount of time to arrive at the starting point because they will interact there.

Therefore,

Cat: 10*3=30
Train: R*3 = D, let us consider this as x.

So we get, R = x/3
The equation is now, after the cat has reached the exit.
Train: R*5 = 80+x => R = 80+x/5
Cat: 10*5=50
R = R = x/3=80+x/5 = x=120
R= 120/3 = 40
40:10 = 4:1

Approach Solution - 3:

Assume the tunnel is 8 km long and the cat is moving at a speed of 8 km/h.
The cat needs three hours to get to A.
The cat needs five hours to get to B.
The time taken by the train, which is 2 hours, is determined by the difference between A and B's times.
Since the train takes two hours and the cat takes eight, the ratio of the speed of train and cat will be,
8 : 2 => 4:1.

“A train approaches a tunnel AB. Inside the tunnel is a cat located” - is a topic that is covered in the quantitative reasoning section of the GMAT. To successfully execute the GMAT Problem Solving questions, a student must possess a wide range of qualitative skills. The entire GMAT Quant section consists of 31 questions. The problem-solving section of the GMAT Quant topics requires the solution of calculative mathematical problems.

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