Question

Kumar, Lakshya, Manoj and Naresh are partners sharing profits in the ratio of 3 : 2 : 1 : 4. Kumar retires and his share is acquired by Lakshya and Manoj in the ratio of 3 : 2. Calculate new profit-sharing ratio and gaining ratio of the remaining partners.

Answer 1

Answer:

19 : 5 : 26

Kumar, Lakshya, Manoj and Naresh are partners sharing profits in the ratio of 3 : 2 : 1 : 4.

Let the profit of Kumar be $K$, Laksuya $L$, Manoj $M$, and Naresh $N$.

*We can let $K=3a$, $L=2a$, $M=a$, $N=4a$.

Since their sum is equal to whole profit,

→ $3a+2a+a+4a=1$

∴ $a=\frac{1}{10}$

Also, we know Lakshya and Manoj gets

the profit of Kumar in the ratio of 3 : 2.

We know the profit of Kumar was $\frac{3}{10}$.

Lakshya gets $\frac{3}{5}$ of $\frac{3}{10}$.

→ Lakshya gets $\frac{9}{50}$.

Kumar gets $\frac{2}{5}$ of $\frac{3}{10}$.

→ Kumar gets $\frac{6}{50}$.

Now add the profit.

*Previous Profit + Kumar's Profit

Lakshya : $\frac{2}{10} +\frac{9}{50} =\frac{19}{50}$

Manoj : $\frac{1}{10}=\frac{5}{50}$

Kumar : $\frac{4}{10} +\frac{6}{50}=\frac{26}{50}$

Their ratio is $19:5:26$.

Answer 2

New profit-sharing ratio and Gaining ratio:

Explanation:

Given,

Kumar, Lakshya, Manoj and Naresh are partners sharing profits in the ratio of 3 : 2 : 1 : 4

Thus, Kumar's share

$=\frac{3}{10}$

After Kumar's retirement, his share acquired by Lakshya and Manoj is in the ratio of 3 : 2.

(acquired by Lakshya and Manoj in 3: 2 )

Share acquisition by Lakshya and Manoj:

Share acquired by Lakshya

$=\frac{3}{10} \times \frac{3}{5}=\frac{9}{50}$

Share acquired by Manoj

$=\frac{3}{10} \times \frac{2}{5}=\frac{6}{50}$

Calculation of New Shares:

Lakshya's New Share

$=\frac{2}{10}+\frac{9}{50}=\frac{19}{50}$

Manoj's New Share

$=\frac{1}{10}+\frac{6}{50}=\frac{11}{50}$

Naresh's share (as retained)

$=\frac{4}{10} or \frac{20}{50}$

New Profit Sharing Ratio

=19: 11: 20

Gaining Ratio =3: 2 (as given in the question)

Thus, the new profit-sharing ratio and gaining ratio of the remaining partners will be 19 : 11 : 20 and 3 : 2 respectively.