Concept: The question tests on the ability to solve a Age Problem
Since we do not have the relation between present present ages, we use 2 variables.
Let age of the younger sister = Y and that of the elder = E
If 1 added to the age of the elder sister, then the ratio of the ages of two sisters becomes 0.5:1.
We get 2Y = E + 1 or
E = 2Y - 1 ... (1)
If 2 is subtracted from the age of the younger one, the ratio becomes 1:3
3Y - 6 = E ... (2)
Equating (1) and (2)
2Y - 1 = 3Y - 6
Y = 6 - 1 = 5