I was chatting with an older friend of mine when I happened to mention the ages of my two children. He said to me, "when your youngest was born your age was the square of the older one. Now your age is the product of both their ages."

I then thought about his age and the ages of his children and replied, "When your youngest was born your age was the product of the older two. Later on your age was the product of the oldest and youngest. Now your age is the product of the younger two."

What are our two ages?

(Assume we all have the same birthday.)

(In reply to computer solution by Charlie)

My  earlier comments regarding your solution were erroneous and was edited out accordingly.

Allow me to record my deepest appreciation for your excellent solution to both the parts.
 
I did not post my solution to the second part as it was very cumbersome and messy.

Edited on January 23, 2013, 2:34 am

Edited on January 23, 2013, 2:36 am

Edited on January 23, 2013, 2:38 am

Posted by K Sengupta on 2013-01-23 02:01:39