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?

(In reply to Problem Solution by K Sengupta)

Let the respective ages of the grandson, son and father in years be  x, y and z.

Then, the father's statement  "My son is as many weeks as my grandson is in days, gives:

7x = y ......(i)

Also, the father's statement that his grandson "is as many months old as I am in years" gives:

z = 12x.....(ii)

But, by conditions of the problem we have:

x+y+z = 100.....(iii)

From (i) and (ii):

z = 12x and y = 7x.
This yields,
12x+7x+x = 100, giving: x = 5, so that:

The age of the grandson = 5 years
The age of the son = 5*7 = 35 years
The age of the father = 5*12 = 60 years.

Posted by K Sengupta on 2007-04-27 14:41:30