Eighty percent of the students in a class (group A) share $40\%$ of the candy equally. The remaining $20\%$ of the students (group B) share the other $60\%$ of the candy equally. The ratio of the amount of candy a student in group A has to the amount of candy a student in group B has is equal to what common fraction?
Suppose that there are $c$ pieces of candy total shared by $s$ students in the class. In group A, there are $.8 \cdot s$ students sharing $.4 \cdot c$ pieces of candy. Dividing the two, we have $\frac{.4c \textnormal{ pieces of candy}}{.8s \textnormal{ students}}$, or $.5\frac{c}{s}$ pieces of candy per student. In group B, there are $.2 \cdot s$ students sharing $.6 \cdot c$ pieces of candy. Dividing the two, we have $\frac{.6c \textnormal{ pieces of candy}}{.2s \textnormal{ students}}$, or $3\frac{c}{s}$ pieces of candy per student. The ratio between the pieces of candy per student in group A and that in group B is $\frac{.5\frac{c}{s}}{3\frac{c}{s}} = \boxed{\frac{1}{6}}$.