From Alwar station a train to Jaipur leaves after every two hours, while a train to Delhi leaves in every nine hours. If trains for both the stations left just now, after how many hours next will the trains for the two stations, leave at the same time again?

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Solution

The correct option is C 18
To find after how many hours will the trains for the two stations, leave at the same time again next, we need to find the LCM.

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...... and so on

Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...... and so on

Hence, Least common multiple (LCM) of 2 and 9 is 18.
So after 18 hours, the trains for both the station will depart at the same time again next.

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