(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 5 : 3. A surrenders 1/20th of this share, whereas B surrenders 1/24th of his share in favour of C, a new partner. Calculate new profit-sharing ration and the sacrificing ratio.

Explanation

A's share `=(5)/(8)`, A surrenders in favour of `C=(1)/(20)xx(5)/(8)=(1)/(32)`
So, A's New share `=(5)/(8)-(1)/(32)-(20-1)/(32)=(19)/(32)`
B's share `=(3)/(8)`, B surrrenders in favour of `C=(1)/(24)xx(3)/(8)=(1)/(64)`
B's New share `=(3)/(8)-(1)/(64)=(24-1)/(64)=(23)/(64)`, C's Share `=(1)/(32)+(1)/(64)=(3)/(64)`
Thus, New Profit-sharing Ratio of A, B and C `=(19)/(32):(23)/(64):(3)/(64)=38:23:3,`
Sacrificing Ratio of A and B `=(1)/(32):(1)/(64),i.e., 2:1`.