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Question

Two trains of equal lengths are running on parallel lines in the same direction at the rate of $$46$$ km/hr and $$36$$ km/hr. The faster train passes the slower train in $$36$$ seconds. What is the length of the trains ?


A
50 m
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B
72 m
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C
80 m
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D
82 m
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Solution

The correct option is A $$50$$ m
To cross each other, two trains have to cover a distance equal to the sum of the lengths of the train.
Let the length of the trains be $$x$$ m each.
So the distance to be covered $$=2x$$.
Now the trains are running int he same direction.
$$\therefore $$ Their relative speed=$$\left( 46-36 \right) $$km/hr.=10km/hr.=$$10\times \dfrac { 5 }{ 18 } $$km/hr.=$$\dfrac { 25 }{ 9 } $$m/sec.
So, the time taken by the trains to cove $$2x$$ m distance
=$$2x\div \dfrac { 25 }{ 9 } $$sec.
$$\therefore $$ By the given conditions,
$$2x\div \dfrac { 25 }{ 9 } sec=36sec$$.
Or $$x=50m$$.
So the length of each train $$=50m$$.

418555_281567_ans.png

Mathematics

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