The sum of the ages of a father and son is 45. Six years ago, their ages were in the ratio 10 : 1. How old will the son be after six years?

Correct option is B

Let the current age of the father be F and the current age of the son be S.

We are given the following conditions: F + S = 45

Six years ago, their ages were in the ratio 10:1, so: $$\frac{F - 6}{S - 6} = 10$$​​

From this equation, we get: F - 6 = 10(S - 6)

Expanding the equation: F - 6 = 10S - 60

Simplifying: F = 10S - 54

Now substitute F = 10S - 54 into the first equation F + S = 45: (10S - 54) + S = 45

Simplifying: 11S - 54 = 45

Solving for S: 11S = 99

​$$S = \frac{99}{11} = 9$$​​

Thus, the current age of the son is 9 years.

After six years, the son's age will be: S + 6 = 9 + 6 = 15 years.