To solve the given question, we need to find out the product of three numbers \( p, q, \text{ and } r \) whose LCM is 30 and HCF is 5, using the provided statements.

Given:

• \(\text{LCM}(p, q, r) = 30\)
• \(\text{HCF}(p, q, r) = 5\)

The relationship between the LCM, HCF, and the product of the numbers is given by the formula:

\(p \times q \times r = \text{LCM}(p, q, r) \times \text{HCF}(p, q, r)\)

Substituting the known values, we have:

\(p \times q \times r = 30 \times 5 = 150\)

Now, let us analyze the given statements:

• Statement I: \( p = 15 \)
• Statement II: \( q = 10 \)

Let's check if either statement alone or both together can determine the product of the three numbers:

Using Statement I alone:

We only know that \( p = 15 \). To find the other two numbers \( q \) and \( r \), we need additional information, as we cannot determine them uniquely from this statement alone.

Using Statement II alone:

Similarly, with \( q = 10 \), we cannot determine \( p \) and \( r \) uniquely without additional information. Therefore, Statement II alone is insufficient.

Using both Statements I and II together:

If \( p = 15 \) and \( q = 10 \), we can find the third number \( r \) using:

\(p \times q \times r = 150 \rightarrow 15 \times 10 \times r = 150\)

Simplifying, we get:

\(150 \times r = 150 \rightarrow r = \frac{150}{150} = 1\)

Thus, the numbers are \( p = 15 \), \( q = 10 \), and \( r = 1 \). Their product is 150, satisfying the condition:

\(15 \times 10 \times 1 = 150\), and the calculated LCM is 30, which matches the given LCM.

Therefore, the correct answer is that the question can be answered by using both the statements together, but cannot be answered using either statement alone.