Question

A and B are partners sharing profits in the ratio of 4:1. A surrenders 1/4th share of his share and B surrenders 1/2 of his share in favour of C , a new partner. What is the sacrificing ratio and the new profit- sharing ratio ?
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Answer 1

ANSWER :

• ❖ If A and B are partners sharing profits in the ratio of 4 : 1 and when C is admitted, A surrenders 1/4 of his share and B surrenders 1/2 of his share in favour of C; then the Sacrificing Ratio of A and B will be 2 : 1 and the New Profit Sharing Ratio of A, B and C will be 6 : 1 : 3.

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SOLUTION :

❒ Given :-

• A and B are partners in a firm sharing profits in the ratio of 4 : 1.

• When C is admitted to the firm, A surrenders 1/4 of his share and B surrenders 1/2 of his shares in favour of C.

❒ To Find :-

• Sacrificing Ratio of A and B = ?

• New Profit Sharing Ratio among A, B and C = ?

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❒ Calculation :-

It is given that,

• Old profit sharing ratio between A and B = 4 : 1.

Thus,

• Old share of A = $\sf{\dfrac{4}{5}}$

• Old share of B = $\sf{\dfrac{1}{5}}$

Again,

• On admission of C, A surrenders $\rm{\dfrac{1}{4}}$ of his share.

Thus,

• ✠ Share surrendered by A = $\sf{\dfrac{1}{4}}$ of $\sf{\dfrac{4}{5}}$

➜ Share surrendered by A = $\sf{\dfrac{1}{4} \times \dfrac{4}{5}}$

➜ Share surrendered by A = $\sf{\dfrac{4}{20}}$

And,

• On admission of C, B surrenders $\rm{\dfrac{1}{2}}$ of his share.

Thus,

• ✠ Share surrendered by B = $\sf{\dfrac{1}{2}}$ of $\sf{\dfrac{1}{5}}$

➜ Share surrendered by B = $\sf{\dfrac{1}{2} \times \dfrac{1}{5}}$

➜ Share surrendered by B = $\sf{\dfrac{1}{10}}$

➜ Share surrendered by B = $\sf{\dfrac{1 \times 2}{10 \times 2}}$

➜ Share surrendered by B = $\sf{\dfrac{2}{20}}$

So,

• ✠ Sacrifice of A = Share surrendered by A

⇒ Sacrifice of A = $\sf{\dfrac{4}{20}}$

And,

• ✠ Sacrifice of B = Share surrendered by B

⇒ Sacrifice of B = $\sf{\dfrac{2}{20}}$

Therefore,

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

➨ Sacrificing Ratio of A and B = $\sf{\dfrac{4}{20}}$ : $\sf{\dfrac{2}{20}}$

➨ Sacrificing Ratio of A and B = 4 : 2

∴ Sacrificing Ratio of A and B = 2 : 1

Also,

We know that,

• $\dag \: \: \underline{ \boxed{ \sf{ \: New \: \: Share = Old \: \: Share - Share \: \: Surrendered \: }}}$

Using this formula,

• ★ New Share of A = Old Share of A - Share Surrendered by A

⇒ New Share of A = $\tt{\dfrac{4}{5} - \dfrac{4}{20}}$

⇒ New Share of A = $\tt{\dfrac{16 - 4}{20}}$

⇒ New Share of A = $\tt{\dfrac{12}{20}}$

Similarly,

• ★ New Share of B = Old Share of B - Share Surrendered by B

⇒ New Share of B = $\tt{\dfrac{1}{5} - \dfrac{2}{20}}$

⇒ New Share of B = $\tt{\dfrac{4 - 2}{20}}$

⇒ New Share of B = $\tt{\dfrac{2}{20}}$

And,

• ★ Share of C = Share Surrendered by A + Share Surrendered by B

⇒ Share of C = $\tt{\dfrac{4}{20} + \dfrac{1}{10}}$

⇒ Share of C = $\tt{\dfrac{4 + 2}{20}}$

⇒ Share of C = $\tt{\dfrac{6}{20}}$

Therefore,

• ✪ New Profit Sharing Ratio of A, B and C = New Share of A : New Share of B : Share of C

➨ New Profit Sharing Ratio of A, B and C = $\tt{\dfrac{12}{20}}$ : $\tt{\dfrac{2}{20}}$ : $\tt{\dfrac{6}{20}}$

➨ New Profit Sharing Ratio of A, B and C = 12 : 2 : 6

∴ New Profit Sharing Ratio among A, B and C = 6 : 1 : 3