The sum of the present ages of a father and his son is 60 years. Six years ago, the age of the father was five times the age of the son. What are the present ages of the father and son respectively? Options 46 years, 14 years 50 years, 10 years 40 years, 20 years 35 years, 25 years
Question
The sum of the present ages of a father and his son is 60 years. Six years ago, the age of the father was five times the age of the son. What are the present ages of the father and son respectively?
Options 46 years, 14 years
50 years, 10 years
40 years, 20 years
35 years, 25 years
Solution
Let's denote the present age of the father as F and the present age of the son as S.
From the problem, we know that:
F + S = 60 (equation 1)
Six years ago, the father was F - 6 years old and the son was S - 6 years old. At that time, the father's age was five times the son's age. So we can write this as:
F - 6 = 5(S - 6) (equation 2)
Now we can solve these equations step by step.
First, let's simplify equation 2:
F - 6 = 5S - 30
F = 5S - 24 (equation 3)
Now we can substitute equation 3 into equation 1:
5S - 24 + S = 60
6S - 24 = 60
6S = 84
S = 14
Substitute S = 14 into equation 1:
F + 14 = 60
F = 46
So, the father is 46 years old and the son is 14 years old. Therefore, the correct option is "46 years, 14 years".
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