To solve this problem, we need to find two numbers that are in the ratio of 15:11 and have a Highest Common Factor (HCF) of 13. Let's go through the solution step-by-step.

Let the two numbers be \(15x\) and \(11x\), based on the given ratio 15:11.

The HCF of \(15x\) and \(11x\) is given as 13. Therefore, \(x\) must be 13 since 13 is the greatest number that divides both numbers entirely. Thus, we can write:

• The first number: \(15x = 15 \times 13 = 195\)
• The second number: \(11x = 11 \times 13 = 143\)

Now we have identified the numbers: 195 and 143.

Let's verify that these numbers meet both conditions (ratio and HCF):

• Ratio: \(\frac{195}{143} = \frac{15}{11}\), which confirms the ratio is 15:11.
• HCF: Since we found \(x = 13\), the HCF condition holds true as the HCF is indeed 13.

Thus, the two numbers are 195 and 143, which matches the correct answer option.

Therefore, the correct answer is 195 and 143.