Explanation:

Let's break it down step by step:

- Let A's present age = x, B’s present age = y.

- Six years ago: (x-6):(y-6) = 7:5 ? (x-6)/(y-6) = 7/5.

- After 4 years: (x+4):(y+4) = 11:9 ? (x+4)/(y+4) = 11/9.

Solving these equations:

- From first: 5(x-6) = 7(y-6) ? 5x-30 = 7y-42 ? 5x-7y = -12.

- From second: 9(x+4) = 11(y+4) ? 9x+36 = 11y+44 ? 9x-11y = 8.

Now, solve the two equations:

- 5x - 7y = -12

- 9x - 11y = 8

Multiply first by 9 and second by 5:

- 45x - 63y = -108

- 45x - 55y = 40

Subtract:

- (45x - 55y) - (45x - 63y) = 40 - (-108) ? 8y = 148 ? y = 18.5

Now substitute in 5x - 7y = -12:

- 5x - 7*18.5 = -12 ? 5x - 129.5 = -12 ? 5x = 117.5 ? x = 23.5

Final answer:

- Present age of A is 23 1/2 years.

Option 3: 23 1/2 years