Explanation:

- LCM (Least Common Multiple) and HCF (Highest Common Factor) are defined for two numbers. Here, LCM = 120 and HCF = 10.

- Let the numbers be \( x \) and \( y \) such that \( x > y \).

- Given \( x - y = 10 \).

- From the relationship between LCM, HCF, and the product of numbers, \( x \times y = \text{LCM} \times \text{HCF} = 120 \times 10 = 1200 \).

- Using \( x = y + 10 \), substitute in the equation:

$$ (y + 10) \times y = 1200 $$

$$ y^2 + 10y = 1200 $$

$$ y^2 + 10y - 1200 = 0 $$

- Solve the quadratic equation to find \( y \). The solution leads to \( y = 30 \) and \( x = 40 \).

- So, the sum of the numbers is \( x + y = 40 + 30 = 70 \).

- Options:

1. 130: Incorrect, doesn't satisfy the conditions.

2. 120: Incorrect, doesn't satisfy the conditions.

3. 70: The correct sum, both the numbers satisfy the conditions.

4. 50: Incorrect, doesn't satisfy the conditions.