scatshouse wrote:

This one has had me stumped for days I just have a complete mental block.

Could anybody help me with the method for solving please?

In July 2006, Becky was two thirds of Mary's age and half of Anna's age. In July 2011, Becky will be three quarters of Mary's age and three fifths of Anna's age.

How old was Becky in July 2005?

It can be done by trial-and-error, but I think this one needs algebra.

Let b, m and a be the ages of the girls in July 2006. Then the first sentence translates as

b = 2/3 m = 1/2 a

In July 2011, their ages will be b+5, m+5 and a+5, so the second sentence translates as

b+5 = 3/4 (m+5) = 3/5 (a+5)

It's enough to consider only two of the girls, say Becky and Anna. (The third is mainly useful as a check.) Substituting a/2 for b in the second equation gives

a/2+5 = 3/5 (a+5)

and solving that gives a = 20 and thus b = 10 and m = 15. And then there's the final trick that you have to subtract 1 to get Becky's age in 2005. After doing a lengthy calculation, so many children forget to go back and check exactly what answer they were asked for.