Question

A, B, and C were partners in a partnership firm sharing profits in the ratio 5:3:2. B retires and the new profit-sharing ratio between A and C is 3:2. Calculate the gaining ratio of A and C.

• A. 3 : 8
• B. 1 : 3
• C. 7 : 2
• D. 1 : 2

Hint:

Gaining ratio is calculated by subtracting old share from new share for each remaining partner.

Answer 1

The Correct Option is D

Step 1: Original profit-sharing ratio
\[ A : B : C = 5 : 3 : 2. \] Step 2: New profit-sharing ratio after B’s retirement
\[ A : C = 3 : 2. \] Step 3: Calculate old shares of A and C
Since total share = 5 + 3 + 2 = 10,
A’s old share = \(\frac{5}{10} = 0.5\),
C’s old share = \(\frac{2}{10} = 0.2\).
Step 4: Calculate new shares of A and C
Sum of new shares \(= 3 + 2 = 5\).
Normalize to 1:
A’s new share = \(\frac{3}{5} = 0.6\),
C’s new share = \(\frac{2}{5} = 0.4\).
Step 5: Calculate gaining ratio
Gaining ratio \(= \text{New share} - \text{Old share}\)
\[ A: 0.6 - 0.5 = 0.1, \quad C: 0.4 - 0.2 = 0.2. \] Step 6: Express gaining ratio as integers
\[ 0.1 : 0.2 = 1 : 2. \] Step 7: Conclusion
Therefore, the gaining ratio of A and C is \(1 : 2\).