A and B are partners sharing profits in the ratio of 5 : 4. They admit C for a `(1)/(10)th` share of profits which he acquires, in equal proportions from both. Find the new profit-sharing ration.

Explanation

C's share of profit in the firm is `(1)/(10)` which he acquires from A and B in equal proportions.
It means A has surrendered `(1)/(2)"of"(1)/(10)=(1)/(20)`
B has surrendered `(1)/(2)"of"(1)/(10)=(1)/(20)`
New Share = Old Share-Share surrendered
A's New Share `=(5)/(9)-(1)/(20)=(100-9)/(180)=(91)/(180)`
B's New Share `=(4)/(9)-(1)/(20)=(80-9)/(180)=(71)/(180)`
C's Share `=(1)/(10)or(18)/(180)`
Thus, New Porfit-sharing Ratio of A, B and C `=(91)/(180):(71)/(180):(18)/(180)=91:71:18`