Brain-Teaser 453

From The Sunday Times, 18th January 1970 [link]

Old Hassan has been at it again! He has thought of a new way of parcelling out his square field between his three sons (Rashid and Riad the twins, and Ali).

Calling the three into his tent on the eve of Ramadhan, he addressed them thus:

“My sons, as I am now 74 years of age, I desire that you shall come into part of your inheritance. I have therefore divided my field into four triangular plots such that we each have an area proportional to our age.”

“To avoid any friction regarding upkeep of fences I have also arranged that none of you shall have a common boundary line with either of your brothers. Further, knowing Rashid and Riad’s objection to being too strongly identified with each other, I have arranged for their plots to be of a different shape.”

The twins are 11 years older than Ali.

How old is Ali?

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