Explanation:

Let's solve step by step:

- Let present ages be A and B.

- 8 years ago: A was (A-8), B was (B-8).

- (A-8)/(B-8) = 4/5 ? 5(A-8) = 4(B-8)

- 12 years hence: (A+12)/(B+12) = 13/15 ? 15(A+12) = 13(B+12)

Let's solve:

Equation 1: 5A-40 = 4B-32 ? 5A-4B = 8

Equation 2: 15A+180 = 13B+156 ? 15A-13B = -24

Let’s solve these:

From Eq 1: 5A - 4B = 8

Multiply Eq 1 by 3 to align coefficients:

15A - 12B = 24

Now subtract Eq 2:

(15A-12B) - (15A-13B) = 24-(-24)

15A-12B-15A+13B = 24+24

B = 48

Options:

- Option 1: 52

- Option 2: 46

- Option 3: 48

- Option 4: 56

Conclusion:

- The present age of B is 48 years.

- Option 3 is correct.