Question

A toy train completes one round of a circular track in $120$ seconds. Another one completes a round in $180$ seconds. Both the trains start together from a station and run in opposite direction.After how many minutes will both the trains meet for the first time at the station from where they started?

Answer 1

Given the first train completes one round of a circular track in $120$ seconds and the second train does so in $180$ seconds.

Now both trains move in the opposite direction in order to find time after which they will meet for the first time we need to take $LCM(120,180)$

$120=2^3\times 3\times 5180=2^2\times 3^2\times 5$

$\therefore LCM(120,180)=360$seconds$=\frac{360}{60}=6$min

$\therefore$ the two trains meet for the first time after $6$ mins from where they started.