A, B, and C are partners sharing profits in the ratio of 3:2:4. A introduces D as a new partner, sharing profits in the new ratio of A:B:C:D = 13:7:4:2. Calculate the new profit sh... A, B, and C are partners sharing profits in the ratio of 3:2:4. A introduces D as a new partner, sharing profits in the new ratio of A:B:C:D = 13:7:4:2. Calculate the new profit sharing ratio. Read more

Steps to Solve

1. Identify the Current Profit Sharing Ratio

The current profit sharing ratio between A and B is given as 3:2.

2. Calculate Total Ratio Units

Add the ratio parts together: $$ 3 + 2 = 5 $$

3. Determine New Partner's Share

C is introduced as a new partner and is allocated a share of $ \frac{1}{6} $ of the profits.

4. Calculate Remaining Profit Share

Calculate the remaining profit share after giving C his share: $$ \text{Remaining share} = 1 - \frac{1}{6} = \frac{5}{6} $$

5. Redistribute Remaining Profit Share

A and B will now share the remaining profit of $ \frac{5}{6} $ according to their original ratio. For A and B:

• For A: $$ \text{A's new share} = \frac{5}{6} \cdot \frac{3}{5} = \frac{3}{6} = \frac{1}{2} $$
• For B: $$ \text{B's new share} = \frac{5}{6} \cdot \frac{2}{5} = \frac{2}{6} = \frac{1}{3} $$

6. Calculate Final Profit Sharing Ratio

Now combine A's, B's, and C's shares:

• A's new share: $ \frac{1}{2} $
• B's new share: $ \frac{1}{3} $
• C's share: $ \frac{1}{6} $

To express these in a common ratio, convert to a common denominator (6):

• A: $ \frac{3}{6} $
• B: $ \frac{2}{6} $
• C: $ \frac{1}{6} $

So the new profit sharing ratio is: $$ 3 : 2 : 1 $$