# Another Ages Problem

phgao
Posers and Puzzles 26 Apr '05 08:53
1. 26 Apr '05 08:53
The sum of the ages of four children of a family is equal to one half of their father's age. The difference of the squares of the ages of the oldest and youngest child equals the father's age which is also equal to twice the sum of the differences of the squares of the ages of the two younger and two older children. In 16 years, the sum of the ages of the children will exceed the father's age by his present age. How old are the fatehr and the four children?
2. 26 Apr '05 11:37
Originally posted by phgao
The sum of the ages of four children of a family is equal to one half of their father's age. The difference of the squares of the ages of the oldest and youngest child equals the father's age which is also equal to twice the sum of the differences of the squares of the ages of the two younger and two older children. In 16 years, the sum of the ages of the ch ...[text shortened]... will exceed the father's age by his present age. How old are the fatehr and the four children?
Father = 32
Children: 2, 3, 5 & 6
3. 26 Apr '05 12:08
Originally posted by Mephisto2
Father = 32
Children: 2, 3, 5 & 6
That doesn't work for the 16 years time scenario, though.

Father: 42yrs 8mths
Child 1: 3yrs 4mths
Child 2: 4yrs 4mths
Child 3: 6yrs 4mths
Child 4: 7yrs 4mths
4. 26 Apr '05 12:15
Originally posted by kody magic
That doesn't work for the 16 years time scenario, though.

Why not?

"In 16 years, the sum of the ages of the children will exceed the father's age by his present age. "

In 16 yyears, the children will be resp. 18, 19,21 & 22. Sum = 80.

Father will be 32+16=48

80-48=32 is the fathers' present age
5. 26 Apr '05 12:22
Good point. That'll teach me to read the question properly!
6. 26 Apr '05 13:19
Originally posted by Mephisto2
Father = 32
Children: 2, 3, 5 & 6
Yep thats right! ðŸ˜€ðŸ˜€