Logical question problem A boy is half as old as the girl will be when the boy’s age is twice the sum of their ages when the boy was the girl’s age. 
How many times older than the girl is the boy at their present age?
This is a logical problem sum.

If $x$ is the boy's age and $y$ is the girl's age, then when the boy was the girl's current age, her age was $2y-x$.  So "twice the sum of their ages when the boy was the girl's age" is $2(3y-x)=6y-2x$.  The boy will reach this age after a further $6y-3x$ years, at which point the girl will be $7y-3x$.  We are told that $x$ is half of this; so $2x=7y-3x$, which means that $x=\frac{7}{5}y$.
