Final answer:
Upon solving the simultaneous equations based on the given conditions, the present ages of the man and his daughter are determined to be 36 years and 14 years respectively. This does not match any of the options provided in the question, indicating a possible error in the choices.
Step-by-step explanation:
The question asks us to determine the present ages of a man and his daughter based on the given conditions that their ages add up to 50 years, and that in eight years the man will be twice as old as his daughter.
Let's denote the man's age as M and the daughter's age as D.
- According to the first condition, we have M + D = 50.
- The second condition can be represented as M + 8 = 2(D + 8).
By solving these simultaneous equations, we can find their present ages.
- From the first equation, we express M in terms of D: M = 50 - D.
- Substitute the value of M in the second equation: (50 - D) + 8 = 2(D + 8).
- Simplify and solve for D: 58 - D = 2D + 16 → 3D = 42 → D = 14.
- Now that we have D, substitute back into the first equation to find M: M = 50 - D = 50 - 14 = 36.
So, the present ages are Man: 36 years, Daughter: 14 years, which is not one of the options provided.
There seems to be an error in the presented choices since none of them meet the conditions given in the problem.