Question

Rushil and Abheer were partners in a firm sharing profits and losses in the ratio of $4:3$. They admitted Sunil as a new partner for $\frac{3}{7}$ share in the profits of the firm, which he acquired $\frac{2}{7}$ share from Rushil and $\frac{1}{7}$ share from Abheer. The new profit sharing ratio of Rushil, Abheer and Sunil will be:

• A. $4:3:3$
• B. $2:1:3$
• C. $2:2:3$
• D. $4:3:1$

Hint:

When a new partner acquires a share from old partners, subtract the sacrificed portion from their old share to obtain the new profit sharing ratio.

Answer 1

The Correct Option is C

Step 1: Determine the old profit sharing ratio.
Rushil and Abheer were sharing profits in the ratio: \[ 4:3 \] This means \[ \text{Rushil's share} = \frac{4}{7}, \quad \text{Abheer's share} = \frac{3}{7} \]
Step 2: Determine the share given to the new partner.
Sunil receives a total share of \[ \frac{3}{7} \] which he acquires as: \[ \frac{2}{7} \text{ from Rushil} \quad \text{and} \quad \frac{1}{7} \text{ from Abheer} \]
Step 3: Calculate the remaining shares of old partners.
Rushil's new share: \[ \frac{4}{7} - \frac{2}{7} = \frac{2}{7} \] Abheer's new share: \[ \frac{3}{7} - \frac{1}{7} = \frac{2}{7} \] Sunil's share: \[ \frac{3}{7} \]
Step 4: Form the new profit sharing ratio.
Thus the new shares are: \[ \frac{2}{7} : \frac{2}{7} : \frac{3}{7} \] Multiplying by 7 to remove denominators: \[ 2 : 2 : 3 \]
Step 5: Conclusion.
Therefore, the new profit sharing ratio of Rushil, Abheer and Sunil is $2:2:3$.
Final Answer: $2:2:3$