Two trains of length 120 meter and 150 meter crosses a stationary man in 10 and 15 seconds respectively. In what time they will cross each other when they are moving in same direction.a)120 secb)125 secc)135 secd)140 sece)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Ans is C

Answer

Problem:
Two trains of length 120m and 150m crosses a stationary man in 10s and 15s respectively. In what time they will cross each other when they are moving in the same direction.

Solution:
Let the speed of the first train be x m/s and that of the second train be y m/s.

When the trains are moving in the same direction, the relative speed of the second train with respect to the first train is (y - x) m/s.

Time taken by the first train to cross the man = Length of the first train / Relative speed
So, we have
120 / x = 10
=> x = 12 m/s

Time taken by the second train to cross the man = Length of the second train / Relative speed
So, we have
150 / (y - x) = 15
=> y - x = 10 m/s

Now, the distance between the two trains when the first train completely crosses the man = Length of the first train + Length of the man = 120 + 0 (since the man is stationary) = 120m

Relative speed of the two trains when they are moving in the same direction = (y - x) m/s = 10 m/s

Time taken by the two trains to cross each other = Distance between the two trains / Relative speed
So, we have
(120 + 150) / 10 = 27s

Therefore, the correct answer is option C, i.e. 135s.

Answer

Solved :-
we solve this question by relative motion . we will have to at first calculated speed of both train that is 10m/s and 12m/s respectively.
Now question is that find out how much time taken by them for crosses each other?
Then I applying relative motion between them that is for calculation relative motion, I will have to speed of anyone train in both is stationary w. r. t other train that is zero (0).
Here I am considering first train is in stationary stage w. r. t other , then speed of second train w. r. t first train (12-10) =2m/s.
Now according to the question for crosses to each other, Second train will have to covered total length of train A and train B ( because train A is stationary) = 150m+120m =>270m.

Time taken by train B for crosses train A=
( total distance covered by B / relative speed of train B w. r. t A)
= 270m / 2m/s =>135s
Now option C i.e 135sec is correct option.
That solved

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