Question

Bhim, Arjun, and Nakul were partners in a firm sharing profits and losses in the ratio of \( 4:3:3 \). With effect from 1st April 2023, they agreed to share profits equally. Due to the change in the profit-sharing ratio, Arjun's gain or sacrifice will be:

• A. Sacrifice \( \frac{1}{30} \)
• B. Gain \( \frac{1}{30} \)
• C. Sacrifice \( \frac{1}{15} \)
• D. Gain \( \frac{1}{15} \)

Hint:

In profit-sharing adjustments, subtract the old share from the new share to determine gain (positive result) or sacrifice (negative result).

Answer 1

The Correct Option is B

The initial profit-sharing ratio is \( 4:3:3 \), and the new profit-sharing ratio is \( 1:1:1 \) (equal sharing). For Arjun: \[ \text{Old Share} = \frac{3}{10}, \quad \text{New Share} = \frac{1}{3} \] Calculate Arjun's sacrifice or gain: \[ \text{Sacrifice or Gain} = \text{New Share} - \text{Old Share} \] Substitute values: \[ \text{Sacrifice or Gain} = \frac{1}{3} - \frac{3}{10} \] Find the LCM of denominators \( 10 \) and \( 3 \), which is \( 30 \): \[ \frac{1}{3} = \frac{10}{30}, \quad \frac{3}{10} = \frac{9}{30} \] \[ \text{Sacrifice or Gain} = \frac{10}{30} - \frac{9}{30} = \frac{1}{30} \] Since the result is positive, it represents a gain. Hence, the correct answer is (B) Gain \( \frac{1}{30} \).