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: Original profit sharing ratio
\[ A : B : C : D = 3 : 2 : 1 : 4 \] Sum of shares = \(3 + 2 + 1 + 4 = 10\) units.
Step 2: A retires and his share is 3/10
A’s share = \(\frac{3}{10}\).
Step 3: B and C acquire A’s share in the ratio 3:2
Total share acquired by B and C = \(\frac{3}{10}\)
B’s additional share = \(\frac{3}{5} \times \frac{3}{10} = \frac{9}{50}\)
C’s additional share = \(\frac{2}{5} \times \frac{3}{10} = \frac{6}{50}\)
Step 4: Calculate new shares
B’s original share = \(\frac{2}{10} = \frac{10}{50}\)
B’s new share = \(\frac{10}{50} + \frac{9}{50} = \frac{19}{50}\)
C’s original share = \(\frac{1}{10} = \frac{5}{50}\)
C’s new share = \(\frac{5}{50} + \frac{6}{50} = \frac{11}{50}\)
D’s share remains = \(\frac{4}{10} = \frac{20}{50}\)
Step 5: New profit sharing ratio
\[ B : C : D = 19 : 11 : 20 \]