Calculation of New Ratio after Admission of C as a Partner

When a new partner is admitted to a partnership, the existing partners' profit sharing ratio changes. In this case, A and B were partners sharing profits in the ratio 3:1, and they admitted C as a new partner. We need to calculate the new ratio assuming that the profit-sharing ratio between A and B has not changed.

Step 1: Calculation of Total Profit
We need to calculate the total profit earned by the partnership before we can determine the new profit sharing ratio. Let's say the total profit earned by the partnership is P.

Step 2: Calculation of Profit Share of A and B
A and B were partners sharing profits in the ratio 3:1, which means A's share is 3/4 of the total profit, and B's share is 1/4 of the total profit. Therefore, A's share is (3/4)P, and B's share is (1/4)P.

Step 3: Calculation of New Profit Sharing Ratio
After admitting C, the new profit sharing ratio will be 3:1:x, where x is the share of C. We know that the profit sharing ratio between A and B has not changed, which means A's share is still 3/4 of the total profit, and B's share is still 1/4 of the total profit. Therefore, we can write:

(3/4)P : (1/4)P : x = 3 : 1 : x

Solving this equation, we get:

x = (1/4)P

Therefore, the new profit sharing ratio is 3:1:1, which means A will get 3/5 of the total profit, B will get 1/5 of the total profit, and C will get 1/5 of the total profit.

Conclusion
In conclusion, after admitting C as a new partner, the new profit sharing ratio is 3:1:1. A will get 3/5 of the total profit, B will get 1/5 of the total profit, and C will get 1/5 of the total profit.

Please give me firstly C's ratio for sharing