2 years ago, the father's age was 6 times of his son's age. 6 years hence the ratio between the ages of father and thif son becomes 10:3. What is the father's present age?A40 YearsB42 YearsC44 YearsD48 Years
Question
2 years ago, the father's age was 6 times of his son's age. 6 years hence the ratio between the ages of father and thif son becomes 10:3. What is the father's present age?A40 YearsB42 YearsC44 YearsD48 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:
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F - 2 = 6 * (S - 2) (Two years ago, the father's age was 6 times the son's age)
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(F + 6) / (S + 6) = 10 / 3 (In six years, the ratio of the father's age to the son's age will be 10:3)
We can solve these two equations to find the values of F and S.
From the first equation, we can express F in terms of S: F = 6S - 10
Substitute F into the second equation:
(6S - 10 + 6) / (S + 6) = 10 / 3
Simplify the equation:
6S - 4 = 10S / 3 + 20
Multiply all terms by 3 to get rid of the denominator:
18S - 12 = 10S + 60
Rearrange the equation:
8S = 72
Solve for S:
S = 9
Substitute S = 9 into the first equation to find F:
F = 6 * 9 - 10 = 44
So, the father's present age is 44 years. The correct answer is C) 44 Years.
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