Question 1090388: The ratio of the age of father and his son 10 years hence will be 5:3,while 10 years ago it was 3:1.the ratio of the age of the son to that of father today is
Answer by greenestamps(13198)   (Show Source):
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First, a traditional algebraic solution....
let f be the father's current age and s be the son's current age
The ratio of their ages 10 years from now will be 5:3
The ratio of their ages 10 years ago was 3:1
"cross multiply" to get two linear equations in s and f
and
Solve the pair of equations by your favorite method to find f=40 and s=20. Then the answer is the ratio of their current ages, which is 40:20, or 2:1.
Next a different algebraic approach...
Since the ratio of their ages 10 years from now will be 5:3, let the father's age then be 5x and the son's age then be 3x. Then their ages 10 years ago are each 20 years less than their ages 10 years from now, so their ages 10 years ago are 5x-20 and 3x-20.
But we know the ratio of their ages 10 years ago was 3:1, so we have
Their ages 10 years from now are 5x and 3x, or 50 and 30, so their current ages are 40 and 20, and the ratio of their current ages is 40:20, or 2:1.
Finally, if you just want to find the answer to the problem and are not required to use formal algebra, this problem can be solved rather easily using logical trial and error.
We know the ratio of their ages 10 years from now will be 5:3. So pick two ages that are in the ratio 5:3 and can be sensible for a father and son. A first guess that is both logical and easy to work with is that their ages 10 years from now will be 50 and 30.
That makes their ages 20 years earlier (that is, 10 years ago) 30 and 10, which agrees with the given information that the ratio of their ages 10 years ago was 3:1. So their current ages are 40 and 20, a ratio of 2:1.
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