Explanation:

- Initially, the boxes A, B, and C have marbles in the ratio 3:5:7. The total number of marbles is 75.

- Let's calculate the number of marbles in each box initially:

- A = \(3x\)

- B = \(5x\)

- C = \(7x\)

- \(3x + 5x + 7x = 75\)

- \(15x = 75\)

- \(x = 5\)

- Therefore, initially:

- A has 15 marbles (3*5),

- B has 25 marbles (5*5),

- C has 35 marbles (7*5).

- Transfer changes:

- 3 marbles are transferred from B to A: A becomes 18, B becomes 22.

- 5 marbles are transferred from C to B: B becomes 27, C becomes 30.

- New counts:

- A = 18, B = 27, C = 30.

- New ratio: 18:27:30 which simplifies to 6:9:10.

Correct Answer: Option 4, 6:9:10