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Difficulty: MediumPuzzle Details

Puzzle IconA husband and wife have a combined age of 91.

The husband is now twice as old as his wife was when he was as old as she is now.

How old are they?

Show Hint Show Answer Print Puzzle
[Ref: ZGZG]  

Answer: Husband = 52, Wife = 39.

If we call the husband's age H, and the wife's W, we know:

   H + W = 91                           (1)

Their age difference is H - W. We know the husband is 2 x (how old his wife was when he was her age), so we need to take their age difference off his current wife's age, as follows:

   2 x (W - (H - W)) = H
     2 x (W - H + W) = H
        2 x (2W - H) = H
             4W - 2H = H
                  4W = 3H
                   W = 3H ÷ 4

Using this in (1) gives:

          H + W = 91

   H + 3(H ÷ 4) = 91

        4H + 3H = 364

             7H = 364

              H = 52

Therefore W = 39.


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