Question

A, B, C and D are partners in a firm sharing profits in the ratio of 3:2:1:4. A retired and his share is acquired by B and C in the ratio 3:2. Calculate the new profit sharing ratio of partners.

• A. 19 : 11 : 20
• B. 3 : 2 : 4
• C. 18 : 12 : 20
• D. 16 : 18 : 12

Hint:

When a partner retires, their share is redistributed among remaining partners in the given ratio, added to their original shares.

Answer 1

The Correct Option is A

Step 1: Initial Profit Distribution Ratio
\[ A : B : C : D = 3 : 2 : 1 : 4 \] Total units of shares = \(3 + 2 + 1 + 4 = 10\).
Step 2: A's Retirement and Share Allocation
A's share, which is \(\frac{3}{10}\) of the total, is now available for redistribution.
Step 3: Redistribution of A's Share
A's entire share of \(\frac{3}{10}\) is distributed between B and C in a 3:2 ratio.
B receives \(\frac{3}{5}\) of A's share: \(\frac{3}{5} \times \frac{3}{10} = \frac{9}{50}\).
C receives \(\frac{2}{5}\) of A's share: \(\frac{2}{5} \times \frac{3}{10} = \frac{6}{50}\).
Step 4: Calculation of New Profit Shares
B's initial share: \(\frac{2}{10}\), equivalent to \(\frac{10}{50}\).
B's updated share: \(\frac{10}{50} + \frac{9}{50} = \frac{19}{50}\).
C's initial share: \(\frac{1}{10}\), equivalent to \(\frac{5}{50}\).
C's updated share: \(\frac{5}{50} + \frac{6}{50} = \frac{11}{50}\).
D's share remains unchanged at \(\frac{4}{10}\), which is \(\frac{20}{50}\).
Step 5: Revised Profit Sharing Ratio
\[ B : C : D = 19 : 11 : 20 \]