13. The father’s age is six times his son’s age. Four years hence, the father’s age will be four times his son’s age. The present ages, in years, of the son and the father are, respectively
4 and 24
5 and 30
6 and 36
3 and 24
Step 1: Define the variables.
Let the son's present age be \(s\) years. Then the father's present age is \(f\) years.
According to the problem, the father is six times the son's age:
\(f = 6s\)
Step 2: Use the condition about their ages after 4 years.
After 4 years, the son's age will be \(s + 4\).
The father's age will be \(f + 4\).
It is given that at that time the father’s age will be four times the son’s age:
\(f + 4 = 4(s + 4)\)
Step 3: Substitute \(f = 6s\) into the equation.
\(6s + 4 = 4(s + 4)\)
Step 4: Simplify.
\(6s + 4 = 4s + 16\)
\(6s - 4s = 16 - 4\)
\(2s = 12\)
\(s = 6\)
Step 5: Find the father's age.
Since \(f = 6s\),
\(f = 6 \times 6 = 36\)
Final Answer:
The son's present age is 6 years, and the father's present age is 36 years.