Answer:
[tex]\text{44 years}[/tex]
Explanation:
[tex]\text{Let the age of father be }x\text{ and son's age be }y.\\\\\text{1st condition:}\\x=2y........(1)\\\\\text{20 years ago, age of father = }x-20\\\text{20 years ago, age of son = }y-20[/tex]
[tex]\text{2nd condition:}\\x-20=12(y-20)\\\\\text{Substituting value of }x\text{ from equation(1),}\\\\2y-20=12y-240\\\text{or, }10y=220\\\text{or, }y=22\\\therefore\ \text{Age of son = }22\text{yrs}\\\text{So, age of father = }2y=2(22)=44\text{yrs}[/tex]
Alternative method:
[tex]\text{Let the age of father be }2x\text{ and the age of son be }x.\\\text{Then,}\\\text{20 years ago, age of father = }2x-20\\\text{20 years ago, age of son = }x-20\\\text{Given,}\\\text{20 years ago, age of father = 12}\times\text{age of son}\\\text{or, }2x-20=12(x-20)\\\text{or, }2x-20=12x-240\\\text{or, }10x=220\\\text{or, }x=22\\\\\therefore\ \text{Present age of father = }2x=2(22)=44\text{yrs}[/tex]
To solve for the father's present age, we set up an equation based on the given relationships, finding that the son is currently 20 years old and the father is 40 years old.
Let's denote the current age of the son as S and the current age of the father as F. According to the problem, the father is currently twice as old as the son, so we can express this relationship as F = 2S.
Twenty years ago, the father was 12 times as old as the son, therefore, F - 20 = 12(S - 20).
To find the present age of the father, we need to solve these two equations simultaneously. Substituting the value of F from the first equation into the second gives us: 2S - 20 = 12S - 240.
Solving for S gives us S = 20.
Since F = 2S, the present age of the father is F = 2*20 = 40 years.
