A milkman adds some amount of water to a pure milk solution to make a $27$liters milk water mixture. He then sells the mixture at the cost price of milk stating no profit earned to his customers, but he uses faulty measurements techniques and gives only $90\%$ of actual value. If in the whole transaction he gains$25\%$ approximately, then the amount of water added initially is.

A $50$ litre mixture of water and alcohol contains $10\%$ alcohol. How much more alcohol must be added to make the strength of alcohol $40\%$ in the new mixture?

There are three kinds of liquids $X,Y,Z$. Three jars $J_1,J_2,J_3$ contain $100$ ml of liquids $X,Y,Z$ respectively. By an operation we mean three steps in the following order:

- stir the liquid in $J_1$ and transfer $10$ ml from $J_1$ into $J_2;$

- stir the liquid in $J_2$ and transfer $10$ ml from $J_2$ into $J_3;$

- stir the liquid in $J_3$ and transfer $10$ ml from $J_3$ into $J_1;$

After performing the operation four times, let $x,y,z$ be the amounts of $X,Y,Z$ respectively in $J_1$. Then