Question

1. A & B are partners in a firm sharing profits in the ratio of 5:3. They admit 'C' as a new partn er for 7h share in the future profit. The new profit sharing ratio will be 4:2:1. 7 Calculate the sacrifice ratio of 'A' and 'B'.​

Answer 1

ANSWER :

• ❖ If A and B are partners in a firm sharing profits in the ratio of 5 : 3; C is admitted as a new partner for 1/7th share in the future profit and the new profit sharing ratio of A, B and C is 4 : 2 : 1; then the Sacrificing Ratio of A and B will be 3 : 5.

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SOLUTION :

❒ Given :-

• A and B are partners in a firm sharing profits in the ratio of 5 : 3.

• C is admitted as a new partner for 1/7th share in the future profit.

• The new profit sharing ratio of A, B and C is 4 : 2 : 1.

❒ To Calculate :-

• Sacrificing Ratio of A and B = ?

❒ Required Formula :-

• $\dag \: \: \underline{ \boxed{ \bold{ \: Sacrifice = Old \: \: Share - New \: \: Share \: }}}$

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❒ Calculation :-

It is given that,

• Old Profit Sharing Ratio of A and B = 5 : 3

So,

• Old Share of A = $\sf{\dfrac{5}{8}}$

• Old Share of B = $\sf{\dfrac{3}{8}}$

And,

• New Profit Sharing Ratio of A, B and C = 4 : 2 : 1

So,

• New Share of A = $\sf{\dfrac{4}{7}}$

• New Share of B = $\sf{\dfrac{2}{7}}$

Using the formula of Sacrifice of a partner, we get,

• ⊚ Sacrifice of A = Old Share of A - New Share of A

⇒ Sacrifice of A = $\tt{\dfrac{5}{8} - \dfrac{4}{7}}$

⇒ Sacrifice of A = $\tt{\dfrac{35 - 32}{56}}$

⇒ Sacrifice of A = $\tt{\dfrac{3}{56}}$

Similarly,

• ⊚ Sacrifice of B = Old Share of B - New Share of B

⇒ Sacrifice of B = $\tt{\dfrac{3}{8} - \dfrac{2}{7}}$

⇒ Sacrifice of B = $\tt{\dfrac{21 - 16}{56}}$

⇒ Sacrifice of B = $\tt{\dfrac{5}{56}}$

Hence,

• ★ Sacrificing Ratio of A and B = Sacrifice of A : Sacrifice of B

➨ Sacrificing Ratio of A and B = $\tt{\dfrac{3}{56}}$ : $\tt{\dfrac{5}{56}}$

∴ Sacrificing Ratio of A and B = 3 : 5