Question

Akshay, Reet and Manya were partners in a firm sharing profits and losses in the ratio of 4 : 3 : 2. With effect from 1st April, 2024, they decided that in future, they will share the profits and losses in the ratio of 2 : 4 : 3. Identify the gain or sacrifice by the partners due to change in the profit sharing ratio from the following:

• A. Akshay’s sacrifice \( \frac{1}{9} \), Reet’s sacrifice \( \frac{1}{9} \), Manya’s gain \( \frac{2}{9} \)
• B. Akshay’s gain \( \frac{1}{9} \), Reet’s gain \( \frac{1}{9} \), Manya’s sacrifice \( \frac{2}{9} \)
• C. Akshay’s sacrifice \( \frac{2}{9} \), Reet’s gain \( \frac{1}{9} \), Manya’s gain \( \frac{1}{9} \)
• D. Akshay’s gain \( \frac{2}{9} \), Reet’s sacrifice \( \frac{1}{9} \), Manya’s sacrifice \( \frac{1}{9} \)

Hint:

When the profit-sharing ratio changes, subtract the new share from the old share for each partner. A positive result means sacrifice; a negative result means gain.

Answer 1

The Correct Option is C

Step 1: Old Ratio = 4 : 3 : 2 \(\Rightarrow\)
Akshay = \( \frac{4}{9} \), Reet = \( \frac{3}{9} \), Manya = \( \frac{2}{9} \)
Step 2: New Ratio = 2 : 4 : 3 \(\Rightarrow\)
Akshay = \( \frac{2}{9} \), Reet = \( \frac{4}{9} \), Manya = \( \frac{3}{9} \)
Step 3: Gain or Sacrifice = Old Share - New Share
- Akshay: \( \frac{4}{9} - \frac{2}{9} = \frac{2}{9} \) (Sacrifice)
- Reet: \( \frac{3}{9} - \frac{4}{9} = -\frac{1}{9} \) (Gain)
- Manya: \( \frac{2}{9} - \frac{3}{9} = -\frac{1}{9} \) (Gain)
Step 4: Total Gain = \( \frac{1}{9} + \frac{1}{9} = \frac{2}{9} \)
Total Sacrifice = \( \frac{2}{9} \)