Question

Kishore and Bimal are partners in a firm sharing profits and losses in the ratio of 4:3. Nand is admitted as a new partner in the firm for $\frac{1{4}$ share in the profits. Kishore and Bimal decide to share profits and losses equally in the future. The sacrificing ratio of Kishore and Bimal will be:}

• A. 1:1
• B. 4:3
• C. 11:3
• D. 3:11

Hint:

The sacrificing ratio is calculated by comparing the old profit-sharing ratio with the new ratio after admission of a partner.

Answer 1

The Correct Option is C

Kishore and Bimal initially share profits and losses in the ratio 4:3. When Nand is admitted for a $\frac{1}{4}$ share in profits, the new profit-sharing ratio needs to be determined.

The firm will now have Nand's share ($\frac{1}{4}$), leaving the remaining $\frac{3}{4}$ to be shared by Kishore and Bimal.

Since Kishore and Bimal now decide to share equally, the new ratio for them will be $\frac{3}{4}$ total profit share equally divided, i.e., $\frac{3}{8}$ each.

To find the sacrificing ratio, calculate the old share, new share, and the difference for both Kishore and Bimal.

Kishore: Old share = $\frac{4}{7}$, New share = $\frac{3}{8}$

Bimal: Old share = $\frac{3}{7}$, New share = $\frac{3}{8}$ 

Calculate the loss in share:

Kishore's sacrifice = $\frac{4}{7} - \frac{3}{8} = \frac{32}{56} - \frac{21}{56} = \frac{11}{56}$

Bimal's sacrifice = $\frac{3}{7} - \frac{3}{8} = \frac{24}{56} - \frac{21}{56} = \frac{3}{56}$

Therefore, their sacrificing ratio is $\frac{11}{56}:\frac{3}{56}$.

Simplifying this gives us a ratio of 11:3.

Thus, the correct sacrificing ratio between Kishore and Bimal is: 11:3.

Answer 2

To calculate the sacrificing ratio of Kishore and Bimal, follow these steps: 

Step 1:} Calculate the old share of Kishore and Bimal. The old profit-sharing ratio of Kishore and Bimal is 4:3. \[ \text{Kishore's old share} = \frac{4}{7}, \quad \text{Bimal's old share} = \frac{3}{7}. \] 

Step 2:} Calculate the new share of Kishore and Bimal.} After Nand’s admission, Kishore and Bimal decide to share profits equally, and Nand takes $\frac{1}{4}$ of the profits. The remaining share is: \[ 1 - \frac{1}{4} = \frac{3}{4}. \] Kishore and Bimal will share the remaining $\frac{3}{4}$ equally: \[ \text{Kishore's new share} = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}, \] \[ \text{Bimal's new share} = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}. \] 

Step 3: Calculate the sacrifice made by Kishore and Bimal. Sacrifice = Old Share $-$ New Share \[ \text{Kishore's sacrifice} = \frac{4}{7} - \frac{3}{8} = \frac{32}{56} - \frac{21}{56} = \frac{11}{56}. \] \[ \text{Bimal's sacrifice} = \frac{3}{7} - \frac{3}{8} = \frac{24}{56} - \frac{21}{56} = \frac{3}{56}. \] 

Step 4: Calculate the sacrificing ratio. \[ \text{Sacrificing Ratio of Kishore and Bimal} = 11:3. \]