Sunday Times Teaser 2874 – An Age-Old Progression

by Angela Newing

Published October 22 2017 (link)

It is my birthday today — the same day as two of my younger relatives, Betty and Charles. I commented that the digits involved in our three ages are all different. Betty noted that the square of her age is equal to my age multiplied by Charles’s age. Then Charles added that on one of our birthdays in the next ten years the sum of our ages will be one hundred.

What are our three ages today?