A Father, son and grandson are walking in the park. A man approaches them and asks for their age. The Father replies, "My son is as many weeks as my grandson is in days, and my grandson is as many months old as I am in years. We are all 100 years together."

How old were each?

It doesn't matter how many days are in a year or how many weeks in a year or how many days or weeks in a month. The ratios stated for the ages are based on determined, constant quantities. The statement that "my son is as many weeks as my grandson is in days" states that the son is seven times as old as the grandson (one week for every day = seven days for every day, or equivalently, seven years for every year). The statement that the grandson is as many months old as the Father is years states that the Father is 12 times as old as the grandson.

Let the grandson have age x years. Then the son has age 7x years and the Father 12x years.

x+7x+12x=100

20x=100

x=5.

So, the grandson is 5, the son 35, and the father 60

Posted by Timothy on 2004-03-26 23:52:27