KVPY SA Exam 2013 Question Paper

There are three kinds of liquids X, Y, Z. Three jars ${\mathit{J}}_1,{\mathit{J}}_2,{\mathit{J}}_3$ contain 100 ml of liquids X, Y, Z, respectively.
By an operation we mean three steps in the following order:
- stir the liquid in ${\mathit{J}}_1$ and transfer 10 ml from ${\mathit{J}}_1$ into ${\mathit{J}}_2$;
- stir the liquid in ${\mathit{J}}_2$ and transfer 10 ml from ${\mathit{J}}_2$ into ${\mathit{J}}_3$;
- stir the liquid in ${\mathit{J}}_3$ and transfer 10 ml from ${\mathit{J}}_3$ into ${\mathit{J}}_1$.
After performing the operation four times, let x, y, z be the amounts of X, Y, Z, respectively, in ${\mathit{J}}_1$ . Then