A binary mixture containing $48$ mass $\%$A and $B$ is to be separated in a plant containing of two stages distillation process. The bottom product from the first distillation column is used as the feed to the second column. The mass composition in percentage of $B$ in the overhead product from the first distillation column is to be $5\%.$ The overhead product from the second column is to contain $98$ mass $\%$ of $A.$ The bottom product from the second column contain $1\%A.$ The fresh feed enters the plant at a rate of $10000k\frac{g}{h}$ and the overhead product from the second column exits at a rate of $2000$ kg$/$h$.$