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
B
72 m
C
80 m
D
82 m

Solution

## The correct option is A $$50$$ mTo 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 $$=50m$$.Mathematics

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