Question

In a train, the ratio of the number of passengers in Cabin A to Cabin B was 1: 2. No passengers got on and got off the train. After 45 passengers moved from Cabin A to Cabin B, the ratio of the number of passengers in Cabin A to Cabin B became 1: 11. How many passengers were there in Cabin A in the end?​

Answer 1

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.