Ten years ago, a father was 4 times as old as his son. Ten years hence, the father will be twice as old as his son. What are their present ages? Options Father: 50 years, Son: 20 years Father: 60 years, Son: 30 years Father: 40 years, Son: 10 years Father: 45 years, Son: 15 years
Question
Ten years ago, a father was 4 times as old as his son. Ten years hence, the father will be twice as old as his son. What are their present ages?
Options Father: 50 years, Son: 20 years
Father: 60 years, Son: 30 years
Father: 40 years, Son: 10 years
Father: 45 years, Son: 15 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 have two equations:
-
F - 10 = 4 * (S - 10) (Ten years ago, the father was four times as old as the son)
-
F + 10 = 2 * (S + 10) (In ten years, the father will be twice as old as the son)
We can solve these two equations to find the values of F and S.
Starting with the first equation:
F - 10 = 4S - 40
=> F = 4S - 30 ---- (equation 3)
Now, substitute equation 3 into the second equation:
4S - 30 + 10 = 2S + 20
=> 4S - 20 = 2S + 20
=> 2S = 40
=> S = 20
Substitute S = 20 into equation 3:
F = 4*20 - 30
=> F = 50
So, the father is 50 years old and the son is 20 years old. Therefore, the correct option is "Father: 50 years, Son: 20 years".
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