Explanation:

- Start with the given ratios:

- The age ratio of A to B is 3:5. Let A = 3x and B = 5x.

- The age ratio of B to C is 3:5. Let B = 3y and C = 5y.

- Since B is common in both ratios, equate the two equations for B:

- 5x = 3y, solving gives x = (3/5)y.

- Substitute x in A's equation:

- A = 3*(3/5)y = (9/5)y.

- Use the total sum:

- A + B + C = 147.

- (9/5)y + 3y + 5y = 147.

- Convert to a single variable:

- (9/5)y + 8y = 147.

- ((9 + 40)/5)y = 147.

- 49y/5 = 147.

- Solve for y:

- y = 147 * (5/49).

- y = 15.

- Calculate B’s age:

- B = 3y = 3 * 15 = 45.

- ? B is 45 years old.

- Correct Answer: Option 3 – 45 years.

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