Explanation:

To solve this, we need to figure out the present ages based on given information.

- 6 years ago, the ratio of A's age to B's age was 7:6. So, let their ages be 7x and 6x then.

- Now, A is 6 years older than C. This translates to: A = C + 6.

- The present sum of B and C's ages is 32: B + C = 32.

With this, let's express A's and B's ages now:

- 6 years ago:

- A = 7x, B = 6x

- Now:

- A = 7x + 6, B = 6x + 6

Given:

- B + C = 32

- A = C + 6

From the age ratio condition:

- A - 6 = 7x

- B - 6 = 6x

From the above equations:

- B = 6x + 6

- C = 32 - B = 32 - (6x + 6) = 26 - 6x

Using A = C + 6:

- \(A = C + 6 = (26 - 6x) + 6 = 32 - 6x\)

- \(7x + 6 = 32 - 6x\)

Solving this:

- \(7x + 6x = 32 - 6\)

- \(13x = 26\)

- \(x = 2\)

Calculate C's present age:

- C = 26 - 6(2) = 26 - 12 = 14

- Correct Answer: Option 2 - 14 years

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