Question

A, B and C were partners in a firm sharing profits in 3:3:2 ratio. They admitted D as a new partner for 4/7 profit. D acquired his share 2/7 from A. 1/7 from B and 1/7 from C. Calculate new profit sharing ratio?​

Answer 1

ANSWER :

• ❖ If A, B and C were partners in a firm sharing profits in 3:3:2 ratio and they admitted D as a new partner for 4/7 profit where D acquired his share 2/7 from A, 1/7 from B and 1/7 from C; then the New Profit Sharing Ratio of A, B, C and D will be 5 : 13 : 6 : 32.

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SOLUTION :

❒ Given :-

• A, B and C were partners in a firm sharing profits in 3 : 3 : 2 ratio.

• D was admitted as a new partner for $\sf{\dfrac{4}{7}}$ profit.

• D acquired his share $\sf{\dfrac{2}{7}}$ from A, $\sf{\dfrac{1}{7}}$ from B and $\sf{\dfrac{1}{7}}$ from C.

❒ To Calculate :-

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

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❒ Calculation :-

It is given that,

• D was admitted as a new partner for $\sf{\dfrac{4}{7}}$ profit.

• D acquired his share $\sf{\dfrac{2}{7}}$ from A, $\sf{\dfrac{1}{7}}$ from B and $\sf{\dfrac{1}{7}}$ from C.

So,

• ✠ D's Share = Share acquires from A + Share acquires from B + Share acquires from C

➜ D's Share = $\sf{\dfrac{2}{7}}$ + $\sf{\dfrac{1}{7}}$ + $\sf{\dfrac{1}{7}}$

➜ D's Share = $\sf{\dfrac{2 + 1 + 1}{7}}$

➜ D's Share = $\sf{\dfrac{4}{7}}$

Again,

• Old Profit Sharing Ratio of A, B and C = 3 : 3 : 2.

So,

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

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

• Old Share of C = $\sf{\dfrac{2}{8}}$

Also,

• Share Sacrificed by A = $\sf{\dfrac{2}{7}}$

• Share Sacrificed by B = $\sf{\dfrac{1}{7}}$

• Share Sacrificed by C = $\sf{\dfrac{1}{7}}$

We know that,

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

Using this formula, we get,

• ★ A's New Share = A's Old Share - Share Sacrificed by A

➨ A's New Share = $\sf{\dfrac{3}{8}}$ - $\sf{\dfrac{2}{7}}$

➨ A's New Share = $\sf{\dfrac{21 - 16}{56}}$

➨ A's New Share = $\sf{\dfrac{5}{56}}$

• ★ B's New Share = B's Old Share - Share Sacrificed by B

➨ B's New Share = $\sf{\dfrac{3}{8}}$ - $\sf{\dfrac{1}{7}}$

➨ B's New Share = $\sf{\dfrac{21 - 8}{56}}$

➨ B's New Share = $\sf{\dfrac{13}{56}}$

• ★ C's New Share = C's Old Share - Share Sacrificed by C

➨ C's New Share = $\sf{\dfrac{2}{8}}$ - $\sf{\dfrac{1}{7}}$

➨ C's New Share = $\sf{\dfrac{14 - 8}{56}}$

➨ C's New Share = $\sf{\dfrac{6}{56}}$

And,

• ★ Share of D = $\sf{\dfrac{4}{7}}$

➨ Share of D = $\sf{\dfrac{4 \times 8}{7 \times 8}}$

➨ Share of D = $\sf{\dfrac{32}{56}}$

Hence,

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

⇒ New Profit Sharing Ratio of A, B, C and D = $\sf{\dfrac{5}{56}}$ : $\sf{\dfrac{13}{56}}$ : $\sf{\dfrac{6}{56}}$ : $\sf{\dfrac{32}{56}}$

∴ New Profit Sharing Ratio of A, B, C and D = 5 : 13 : 6 : 32