Twelve years from now a mother will be twice as old as her daughter. Today the two ages together come to 60 years. How much older is the mother than the daughter?

Let the daughter be $d$ and the mother $m$ today. In twelve years, $m+12=2(d+12)$, so $m=2d+12$. With $m+d=60$, we get $3d+12=60,d=16$ and $m=44$, a gap of 28 years. Check: in twelve years they will be 56 and 28, and $56=2\times 28$. 44 and 16 are the two ages, not the gap the question asks for. 20 comes from applying 'twice as old' to TODAY, splitting 60 as 40 and 20; but that condition belongs to twelve years from now, by which time the doubling has become easier to satisfy.