Question

The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. Find the present ages of the son and the father.

Answer 1

The present age of the son is S = 6 years, and the father's age is F = 36 years.

Step-by-step explanation:

Let's denote the present age of the son as S years and the father as F years. According to the problem, we're given two conditions:

1. The father's age is six times his son's age: F = 6S.

2. Four years from now, the father's age will be four times his son's age: F + 4 = 4(S + 4).

We'll use these equations to find the values of S and F.

Starting with the first equation, F = 6S, and substituting this into the second equation, we get:

6S + 4 = 4(S + 4).

Expanding the equation:

6S + 4 = 4S + 16

Rearranging terms:

6S - 4S = 16 - 4

2S = 12

S = 6

Now that we have found the value of S (son's age) as 6, let's substitute this back into the equation F = 6S to find F (father's age):

F = 6 * 6

F = 36

Therefore, the present age of the son (S) is 6 years, and the father's age (F) is 36 years. This satisfies both conditions given in the problem statement.