Question

Anisha, Deepa, and Charu were partners sharing profits and losses in the ratio of 5:3:2. On 31st March 2024, they decided to change their profit-sharing ratio to 2:3:5. Each partner's gain or sacrifice due to the change in profit-sharing ratio will be:

• A. Anisha’s sacrifice \(\frac {3}{10}\) ; Charu’s gain \(\frac {3}{10}\)
• B. Anisha’s gain \(\frac {3}{10}\) ; Charu’s sacrifice \(\frac {3}{10}\)
• C. Anisha’s sacrifice \(\frac {3}{10}\); Deepa’s gain \(\frac {3}{10}\)
• D. Deepa’s gain \(\frac {3}{10}\); Charu’s sacrifice \(\frac {3}{10}\)

Hint:

Remember: To calculate sacrifice or gain, use the formula \texttt{Old Share - New Share}. - A positive result means a sacrifice. - A negative result means a gain. The total sacrifice must always equal the total gain.

Answer 1

The Correct Option is A

To calculate each partner's gain or sacrifice, we need to compare their old and new profit-sharing ratios. The formula for calculating gain or sacrifice is: \[ \text{Sacrifice or Gain} = \text{Old Share} - \text{New Share} \] where a positive result indicates a sacrifice, and a negative result indicates a gain. Step 1: Express the Old and New Ratios - Old Ratio (Anisha : Deepa : Charu) = 5:3:2, or \( \frac{5}{10} : \frac{3}{10} : \frac{2}{10} \) - New Ratio (Anisha : Deepa : Charu) = 2:3:5, or \( \frac{2}{10} : \frac{3}{10} : \frac{5}{10} \) Step 2: Calculate the Change for Each Partner - Anisha's Change: \[ \text{Anisha's Sacrifice} = \frac{5}{10} - \frac{2}{10} = +\frac{3}{10} \text{ (Sacrifice)} \] - Deepa's Change: \[ \text{Deepa's Change} = \frac{3}{10} - \frac{3}{10} = 0 \text{ (No change)} \] - Charu's Change: \[ \text{Charu's Gain} = \frac{2}{10} - \frac{5}{10} = -\frac{3}{10} \text{ (Gain)} \] Step 3: Conclusion - Anisha sacrifices \( \frac{3}{10} \) of her share. - Charu gains \( \frac{3}{10} \) of the share. - Deepa's share remains unchanged. Thus, the correct answer is Option (A), where Anisha sacrifices \( \frac{3}{10} \), and Charu gains \( \frac{3}{10} \).