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 was \( 4:3:3 \), changing to a new equal sharing ratio of \( 1:1:1 \). For Arjun, the old share was \( \frac{3}{10} \) and the new share is \( \frac{1}{3} \). Arjun's sacrifice or gain is calculated as New Share - Old Share. Substituting the values, this becomes \( \frac{1}{3} - \frac{3}{10} \). The least common multiple of 10 and 3 is 30. Thus, \( \frac{1}{3} \) becomes \( \frac{10}{30} \) and \( \frac{3}{10} \) becomes \( \frac{9}{30} \). The sacrifice or gain is \( \frac{10}{30} - \frac{9}{30} = \frac{1}{30} \). As the result is positive, Arjun has a gain of \( \frac{1}{30} \). Therefore, the correct option is (B) Gain \( \frac{1}{30} \).