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: Initial profit distribution
\[ A : B : C = 5 : 3 : 2. \] Step 2: Revised profit distribution post B's departure
\[ A : C = 3 : 2. \] Step 3: Determination of A and C's original profit shares
Total initial shares = 5 + 3 + 2 = 10.
A's original share = \(\frac{5}{10} = 0.5\),
C's original share = \(\frac{2}{10} = 0.2\).
Step 4: Calculation of A and C's updated profit shares
Total new shares = 3 + 2 = 5.
Normalized to a total of 1:
A's new share = \(\frac{3}{5} = 0.6\),
C's new share = \(\frac{2}{5} = 0.4\).
Step 5: Calculation of the gain ratio
Gain ratio = New share - Old share
\[ A: 0.6 - 0.5 = 0.1, \quad C: 0.4 - 0.2 = 0.2. \] Step 6: Expression of the gain ratio in whole numbers
\[ 0.1 : 0.2 = 1 : 2. \] Step 7: Final Result
Consequently, the gain ratio between A and C is \(1 : 2\).