Dr. Johnson asked his friend how old his son was, and got the following answer: “My son is five times as old as my daughter, and my wife is five times as old as my son. I am twice as old as my wife, whereas my grandmother, who is celebrating her eighty-first birthday is as old as all of us put together.”
How old was his friend’s son?
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S= son’s age, D=daughter’s age, W=wife’s age, F=friend’s age. Then, 81=D + S + W + F.
We have that S=5D, W=5S=25D, F=2W= 50D. Hence, 81= D+ 5D+25D + 50D, so 81=81D. Therefore, D=1, and S=5.