Brainteaser 1649: Ages and ages!

From The Sunday Times, 17th April 1994 [link]

Today is the birthday of both Mary and Nelly, so it is a good time to have a conundrum about their ages.

When Mary was one third of the age she is today, Nelly was half the age that Mary was when Nelly was the age that Mary was when Nelly was the age that Mary was when Nelly was a quarter of the age she is today.

If neither of them is yet eligible for an old-age pension, how old are they both today?

This puzzle was included in the book Brainteasers (2002, edited by Victor Bryant).

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