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Can you solve this without making any equation??

In the above image a boy is at a point in the tunnel AB, dividing it in the ratio 2:3. A train is approaching the side A with a constant speed. Now at a particular instant of time, the situation is such that if the boy runs towards A the train enters the tunnel just as he come out. And if he decides to go towards B, then the train and the boy both will come out at the same time. Our job is to find the ratio between their speeds. The real task is doing this by the most elementary method that is possible.

Note by Sanjeet Raria
2 years, 9 months ago

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Well, when the boy covers 2 m , the train reaches A. Now let the boy run towards B. When he'd cover 2m of distance the train would just reach A. Now pause here and take a look, the boy has 1m to go next and while he will cover this unit distance, the train will be covering 5m and they will come out together. That means in the same amount of time the boy covers 1m and train covers 5m. It means ratio of their velocity is 1:5 Sanjeet Raria · 2 years, 9 months ago

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@Sanjeet Raria Ohh....this is really a very nice way of thinking...nice solution Milind Joshi · 2 years, 9 months ago

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5:1 Milind Joshi · 2 years, 9 months ago

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@Milind Joshi Your answer is correct but here I'm more concerned towards the method of solving it. Sanjeet Raria · 2 years, 9 months ago

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@Sanjeet Raria Suppose speed is same....1:1..and take the length of the tunnel as 5m...so dist btwn man to A is 2m and man to B is 3m....now if ratio is 1:1 then if man runs towards A he will cover 2m and train will also cover 2m bcoz speed is same....so train is 2m away from the tunnel....now in 2nd case man runs towards B so he will cover 3m and train will also cover 3m..but in this case train will be at 1m away from pnt A in the direction of B...so our assumption 1:1 is incorrect....let the ratio 2:1...then in 1st case we came to know that train is 4m away from pnt A...and when man will be at B train will be 2m away from pnt A towards B....so 2:1 is also wrong....by this way we can find that 5:1 satisfies both cases...and it is the right ans...soln is quite lengthy but it is easy... Milind Joshi · 2 years, 9 months ago

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@Milind Joshi Well, when the boy covers 2 m , the train reaches A. Now let the boy run towards B. When he'd cover 2m of distance the train would just reach A. Now pause here and take a look, the boy has 1m to go next and while he will cover this unit distance, the train will be covering 5m and they will come out together. That means in the same amount of time the boy covers 1m and train covers 5m. It means ratio of their velocity is 1:5 Sanjeet Raria · 2 years, 9 months ago

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@Milind Joshi This is very long in its sense man! Sanjeet Raria · 2 years, 9 months ago

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