Suman, Shubham and Siya were partners in a firm sharing profits and losses in the ratio of $\displaystyle 5$ : $\displaystyle 3$ : 2. Shubham retired from the firm and Suman and Siya decided to continue the business. Their gaining ratio was $\displaystyle 3$ : 2. Calculate the new profit sharing ratio of Suman and Siya.

Old Profit Sharing Ratio Suman Shubham Siya $\displaystyle 5$ $\displaystyle 3$ $\displaystyle 2$ $\displaystyle 10$ $\displaystyle 10$ $\displaystyle 10$ $\displaystyle 3$ Shubham’s share = $\displaystyle 10$ Gaining ratio of Suman and Siya = $\displaystyle 3$ : $\displaystyle 2$ $\displaystyle 3$ $\displaystyle 3$ $\displaystyle 9$ Suman’s gain =  = $\displaystyle 5$ $\displaystyle 10$ $\displaystyle 50$ $\displaystyle 2$ $\displaystyle 3$ $\displaystyle 6$ Siya’s gain =  = $\displaystyle 5$ $\displaystyle 10$ $\displaystyle 50$ New share= Old Share + Gain $\displaystyle 5$ $\displaystyle 9$ Suman’s new share = + $\displaystyle 10$ $\displaystyle 50$ $\displaystyle 34$ = $\displaystyle 50$ $\displaystyle 2$ $\displaystyle 6$ Siya’s new share = + $\displaystyle 10$ $\displaystyle 50$ $\displaystyle 16$ = $\displaystyle 50$ New profit sharing ratio of Suman and Siya : $\displaystyle 34$:$\displaystyle 16$ = $\displaystyle 17$ : $\displaystyle 8$