Question : X, Y and Z are partners in proportion of $\frac{3}{6}, \frac{2}{6}$ and $\frac{1}{6}$ respectively. D was admitted to the firm as a new partner with $\frac{1}{6}$ th share. The new profit-sharing ratios of the partners will be
Option 1: 15:10:5:6
Option 2: 3:2:1:1
Option 3: 15:10:5:1
Option 4: None of the above
Correct Answer: 15:10:5:6
Solution : Answer = 15:10:5:6
Calculation of new profit sharing ratios :
Let total profit be =1
Share given to D= $\frac{1}{6}$
Remaining Share= $1-\frac{1}{6}=\frac{5}{6}$
Now the old partners will share this remaining profit in their old profit-sharing ratios:
Hence,
X's Share $=\frac{3}{6}$ of $\frac{5}{6}=\frac{5}{12}$
y's Share $=\frac{2}{6}$ of $\quad \frac{5}{6}=\frac{5}{18}$
Z's Share $=\frac{1}{6}$ of $\frac{5}{6}=\frac{5}{36}$
D's Share $=\frac{1}{6}$
Thus, the new profit-sharing ratio of X, Y, Z and D will be :
= $\frac{5}{12}: \frac{5}{18}: \frac{5}{36}: \frac{1}{6}=\frac{15: 10: 5: 6}{36}$=15: 10: 5: 6.
Hence, the correct option is 1.
