Question - Buses and Timings

Let the time taken for Bus A to complete a round trip be \( t_A \) and for Bus B be \( t_B \).

Assuming Bus A takes 6 minutes for a trip, we have \( t_A = 6 \) minutes.

Assuming Bus B takes double the time of Bus A, \( t_B = 2 \times t_A = 2 \times 6 = 12 \) minutes.

To find the least common multiple (LCM) of 6 and 12:

LCM(6, 12) = 12 minutes.

Therefore, both buses will be back at the station together after 12 minutes.