The given problem involves the ratio of ages between a man and his son. Initially, the ratio is stated as 3:1, indicating that for every 3 years the man ages, his son ages 1 year.
After a span of 15 years, we are told that the age ratio will be 2:1. This means that after 15 years, for every 2 years the man ages, his son ages 1 year.
To find the age of the man, we need to determine his current age. Using the given ratios, we can set up the following equation:
3x + 15 = 2x
Simplifying the equation, we get:
x = 15
Therefore, the son`s current age is 15 years. Since the ratio of ages is 3:1, the man`s age would be three times that of the son`s age, which equals 45 years.
Hence, the correct answer is option 1, which states that the age of the man is 45 years.