Question

Q. 2 (A). P and Q are partners sharing profits and losses in the ratio of 4 : 3. They admit R as partner for a 1/7th share in profits which he acquires equally from P and Q. Calculate new profit sharing ratio of the partners.
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Answer 1

Given data:

• P and Q are partners in a firm, sharing profits and losses in the ratio 4:3.
• R is admitted into the firm for 1/7th of the shares.
• R gets his share from P and Q equally.

To find: The new profit-sharing ratio.

Answer:

• P's old share = 4/7
• Q's old share = 3/7
• R's share = 1/7

Since R gets 1/7 from P and Q equally, 1/7 will need to be divided by 2 [∵ there are 2 old partners].

From P, R gets:

• 1/7 ÷ 2 = 1/7 × 1/2 = 1/14

From Q, R gets:

• 1/7 ÷ 2 = 1/7 × 1/2 = 1/14

Calculation of the new profit-sharing ratio:

New ratio = Old ratio - Ratio surrendered

For P:

• New ratio = 4/7 - 1/14 = (8 - 1)/14 = 7/14

For Q:

• New ratio = 3/7 - 1/14 = (6 - 1)/14 = 5/14

For R:

• New ratio = 1/7, or 2/14

Therefore, the new profit-sharing ratio is 7:5:2.

Answer 2

Answer:

The new profit-sharing ratio of the partners is 4:5:2.

Explanation:

Given:

P and Q are partners sharing profits and losses in the ratio of 4 : 3.

They admit R as a partner for a 1/7th share in profits which he acquires equally from P and Q.

To find:

Calculate the new profit sharing ratio of the partners.

Profit acquired by R from P is = $\frac{1}{2}*\frac{1}{7}=\frac{1}{14}$,

Profit acquired by R from Q is = $\frac{1}{2}\times \frac{1}{7}=\frac{1}{14}$,

New profit of share of P = $\frac{4}{7}-\frac{1}{14}=\frac{8-14}{14}$

                                                       = $\frac{4}{14}$

New profit share of Q = $\frac{3}{7}-\frac{1}{14}$,

                                     = $\frac{6-1}{14}$,

                                     = $\frac{5}{14}$

New profit share of R = $\frac{1}{7}$.

Therefore, the new profit ratio =  $\frac{4}{14}:\frac{5}{14}:\frac{1}{7}$

                                                    = $\frac{2}{7}:\frac{5}{14}:\frac{1}{7}$

                                                    = 4 : 5 : 2

Hence, the new profit ratio of the partners is 4:5:2.

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