(Old Partners Sacrifice Fraction of their Shares in Favour of New Partner).
A and B are partners in a firm sharing profits and losses in the ration of 3:2 A surrenders `(1)/(5)th` of his share, whereas B surrenders `(2)/(5)th` of his share in favour of C, the new partner. Calculate new profit-sharing ratio.

Explanation

A's share `=(3)/(5)`, A surrenders in favour of `C=(3)/(5)xx(1)/(5)=(3)/(25)`
B's share `=(2)/(5)`, B surrenders in favour of `C=(2)/(5)xx(2)/(5)=(4)/(25)`
New Share =Old Share-Share surrendered
So, A's New share `=(3)/(5)-(3)/(25)=(15-3)/(25)=(12)/(25)`
So, B's New share `=(2)/(5)-(4)/(25)=(10-4)/(25)=(6)/(25)`
C's share is the sum of shares surrendered by A and B `B=(3)/(25)+(4)/(25)=(7)/(25)`
Thus, New Profit-sharing Ratio A, B and C `=(12)/(25):(6)/(25):(7)/(25)=12:6:7`