X and y are partners sharing profits and losses in the proportion of 3...
Introduction:
X and Y are partners in a business and share profits and losses in the ratio of 3/5:2/5. They decide to admit Z into the partnership and give him a share of goodwill, which he acquired 3/20 from X and 1/20 from Y. The profit for the first year of the new partnership is Rs. 100,000.
Calculation of Share of Profits:
To calculate the share of profits for X and Y, we need to first calculate the total profit for the year. Since the profit is Rs. 100,000, we can calculate the share of profits for each partner as follows:
X's share = (3/5) * 100,000 = Rs. 60,000
Y's share = (2/5) * 100,000 = Rs. 40,000
Calculation of Z's Share:
To calculate Z's share, we first need to calculate the total value of goodwill. We know that Z's share of goodwill is 1/5, which means that the total value of goodwill is:
Goodwill = (1/5) * Total Capital
Total Capital = (5/1) * Goodwill
Now, we also know that Z acquired 3/20 of the goodwill from X and 1/20 from Y. So, we can write the following equation:
(3/20) * Total Capital = X's Share of Goodwill
(1/20) * Total Capital = Y's Share of Goodwill
Solving these equations simultaneously, we get:
Total Capital = Rs. 60,000
X's Share of Goodwill = Rs. 9,000
Y's Share of Goodwill = Rs. 3,000
Therefore, Z's share of goodwill is:
Z's Share of Goodwill = Total Goodwill - (X's Share + Y's Share)
Z's Share of Goodwill = Rs. 48,000 - Rs. 12,000
Z's Share of Goodwill = Rs. 36,000
Final Calculation of Profit Sharing:
Now that we have calculated the share of profits and goodwill for each partner, we can calculate the final profit sharing ratio as follows:
X's share = Rs. 60,000 (Profit) + Rs. 9,000 (Goodwill) = Rs. 69,000
Y's share = Rs. 40,000 (Profit) + Rs. 3,000 (Goodwill) = Rs. 43,000
Z's share = Rs. 36,000 (Goodwill) + Rs. 20,000 (1/5 of Profit) = Rs. 56,000
Therefore, the final profit sharing ratio is:
X : Y : Z = 69,000 : 43,000 : 56,000
Conclusion:
In conclusion, we can say that X and Y are partners sharing profits and losses in the ratio of 3/5:2/5. They admit Z into the partnership and give him a share of goodwill, which he acquired 3/20 from X and 1/20 from Y. The profit for the first year of the new partnership is Rs. 100,000. The final profit sharing ratio is X : Y : Z