Explanation:

- To find the sum of two numbers given their Highest Common Factor (HCF) and Least Common Multiple (LCM), we use the relationship: HCF × LCM = Product of the numbers.

- Here, HCF = 17 and LCM = 561.

- So, the product of the two numbers is 17 × 561 = 9537.

- Let the two numbers be 17a and 17b, where a and b are co-prime (since HCF is 17).

- Then, 17a × 17b = 9537, simplifying to a × b = 33.

- The possible pair for (a, b) given that they are co-prime is (3, 11).

- Therefore, the numbers are 17 × 3 = 51 and 17 × 11 = 187.

- The sum is 51 + 187 = 238.

- Options:

- Option 1, 387: Incorrect, doesn't match the sum.

- Option 2, 238: Correct, matches the sum.

- Option 3, 268: Incorrect, doesn't match the sum.

- Option 4, 340: Incorrect, doesn't match the sum.