Let's assume the initial number of passengers in Cabin A and Cabin B to be x and 2x respectively.
After 45 passengers moved from Cabin A to Cabin B, the number of passengers in Cabin A became (x-45) and the number of passengers in Cabin B became (2x+45).
Now, as per the given condition, the ratio of the number of passengers in Cabin A to Cabin B became 1:11. So, we can write:
(x-45)/(2x+45) = 1/11
Solving for x, we get:
11(x-45) = 2x+45
11x - 495 = 2x + 45
9x = 540
x = 60
Therefore, the initial number of passengers in Cabin A was x = 60, and the initial number of passengers in Cabin B was 2x = 120.
After 45 passengers moved from Cabin A to Cabin B, the number of passengers in Cabin A became (x-45) = 15, and the number of passengers in Cabin B became (2x+45) = 225.
Hence, the final number of passengers in Cabin A was 15.