Final answer:
The correct answer is option A. To solve this problem, assign variables to the ages of the father and the son. Set up a system of equations using the information given and solve for the current ages. The ratio of their present ages is 5 : 2.
Step-by-step explanation:
To solve this problem, let's start by assigning variables to the ages of the father and the son. Let's say the father's age is F and the son's age is S.
According to the problem, the age of the father 10 years ago was thrice the age of his son. This can be expressed as:
F - 10 = 3(S - 10)
Simplifying this equation, we get F - 10 = 3S - 30
Next, the problem says that ten years hence, the father's age will be twice that of his son. This can be expressed as:
F + 10 = 2(S + 10)
Simplifying this equation, we get F + 10 = 2S + 20
Now we have a system of two equations:
F - 10 = 3S - 30
F + 10 = 2S + 20
We can solve this system of equations to find the values of F and S, which represent the current ages of the father and the son. Once we have those values, we can calculate the ratio of their present ages.
By solving the system, we find that the father's current age (F) is 50 and the son's current age (S) is 20. Therefore, the ratio of their present ages is 5 : 2.