Answer: Option B
Given information:

• HCF of two numbers = 24
• LCM of two numbers = 1344
• Difference between the numbers = 80

We need to find the sum of the two numbers.
Let the two numbers be a and b, such that a > b. Then we have the following relationships:a * b = HCF * LCM = 24 * 1344 = 32256 --- (1)a - b = 80 --- (2)
We can use equation (2) to express one variable in terms of the other:a = b + 80
Substituting this into equation (1), we get:(b + 80) * b = 32256b^2 + 80b - 32256 = 0
We can solve for b using the quadratic formula:b = (-80 ± √(80^2 + 4*32256)) / 2b = (-80 ± 496) / 2
We take the positive value of b, since a > b:b = 208
Using equation (2), we can find the value of a:a = b + 80 = 288
Therefore, the sum of the two numbers is:a + b = 288 + 208 = 496
Thus, the correct answer is option B (368).
To summarize, we used the following concepts/formulas:

• HCF * LCM = product of two numbers
• Quadratic formula to solve for roots of a quadratic equation.

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