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 $\frac{1}{30}$.