Using Statement-I alone: Statement-I tells us that the age of P is greater than the age of Q, i.e., $P > Q$. However, this does not give a unique solution, as there are multiple possible combinations of P and Q where P is greater than Q. For example:

• If P = 81, Q = 18, the condition holds.
• If P = 72, Q = 27, the condition holds.

Therefore, Statement-I alone is not sufficient to determine the exact difference in their ages.

Using Statement-II alone: Statement-II provides a mathematical relationship between the sum and difference of their ages:

The sum of their ages is 11/6 times their difference:

$P + Q = (\frac{11}{6}) \times (P - Q)$

Substituting the values of P and Q ($P = 10x + y$ and $Q = 10y + x$), we can simplify the equation:

$(10x + y) + (10y + x) = (\frac{11}{6}) \times ((10x + y) - (10y + x))$

Simplifying the equation gives:

$11(x + y) = (\frac{11}{6}) \times 9(x - y)$

$6(x + y) = 9(x - y)$

$2(x + y) = 3(x - y)$

$x = 5y$

Given that x and y must be digits (i.e., between 0 and 9), the only solution that satisfies this equation is when y = 1 and x = 5. Therefore, P = 51 and Q = 15.

The difference in their ages is:

$P - Q = 51 - 15 = 36$

Thus, Statement-II alone is sufficient to answer the question.

Conclusion: The question can be answered by using Statement-II alone, but Statement-I alone is not sufficient.