Explanation:

To find the present age of B, follow these steps:

- Let the present ages of A and B be 7x and 11x respectively.

- After 10 years, A's age will be 7x + 10 and B's age will be 11x + 10.

- According to the problem, after 10 years the ratio of their ages will be 13 : 19.

So, we set up the equation:

$$

\frac{7x + 10}{11x + 10} = \frac{13}{19}

$$

- Cross-multiply to solve for x:

$$

19(7x + 10) = 13(11x + 10)

$$

- Simplifying the equation:

$$

133x + 190 = 143x + 130

$$

- Rearrange to find x:

$$

143x - 133x = 190 - 130

$$

$$

10x = 60

$$

$$

x = 6

$$

- Now, the present age of B is 11x = 11 * 6 = 66 years.

- Check the options:

- ? Option 3: 66 years – This matches the calculation.

- Option 1, 2, 4 don't match the calculation.

- Option 5 is for if none of these is correct.

Therefore, the correct option is Option 3: 66 years.

?