# Daughters' Ages Quiz Puzzle Answer

In The Jolly Quizmaster we were talking to the landlord's wife who told us some facts about her age and the ages of her daughters. Knowing we liked a puzzle she asked us to work them out.

Currently, her age in whole years is three times the sum of her three daughters' ages, again in whole years.

Clearly the ratio will decrease as the years pass, and in eleven years time her age in whole years will equal the sum of her three daughters' ages, again in whole years.

The age in years of the eldest daughter is now equal to the product of the ages in years of the other two daughters.

None of the three children are the same age.

How old are the landlord's wife and the three daughters?

If M is the mother's age and D the sum of the daughters' ages then now M = 3D.

And in eleven years time M + 11 = D + 33, and so M = D + 22.

If M is 3D and D + 22, then 3D = D + 22, and 2D = 22, so the sum of the daughters' ages now is 11.

Thus the landlord's wife is 33.

As the children are all different ages, they must be 6, 3 and 2.