Question

Suresh and Ramesh were partners in a firm sharing profits in 5:3 ratio. On 1-4-2018 they Deepak as a new partner for 1/4th share. On 31st July, 2018 Karan was admitted as a new pante 1/6th share which he acquired equally from Suresh, Ramesh and Deepak. Calculate the new profit sharing ratio of Suresh, Ramesh, Deepak and Karan.​

Answer 1

ANSWER :

• ❖ The New Profit Sharing Ratio of Suresh, Ramesh, Deepak and Karan will be 119 : 65 : 56 : 48.

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SOLUTION :

❒ Given :-

• Suresh and Ramesh were partners in a firm sharing profits in 5 : 3 ratio.

• Deepak was admitted as a new partner for $\sf{\dfrac{1}{4}}$ th share of profit on 1st April, 2018.

• Karan was admitted as a new partner for $\sf{\dfrac{1}{6}}$ th share of profit on 31st July, 2018.

• Karan acquired his share equally from Suresh, Ramesh and Deepak.

❒ To Calculate :-

• New Profit Sharing Ratio of Suresh, Ramesh, Deepak and Karan = ?

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❒ Calculation :-

It is given that,

• Deepak was admitted as a new partner for $\sf{\dfrac{1}{4}}$ th share of profit.

Suppose,

• Total Profit of the firm = 1

Then,

• Share of Deepak = $\sf{\dfrac{1}{4}}$ th of 1

⟹ Share of Deepak = $\sf{\dfrac{1}{4}}$

So,

• Remaining Share = 1 - Share of Deepak

⟹ Remaining Share = 1 - $\sf{\dfrac{1}{4}}$

⟹ Remaining Share = $\sf{\dfrac{3}{4}}$

This remaining share of $\sf{\dfrac{3}{4}}$ will be shared by Suresh and Ramesh in their old ratio.

Here,

• Old Profit Sharing Ratio of Suresh and Ramesh = 5 : 3.

So,

• ⍟ New Share of Suresh = $\sf{\dfrac{5}{8}}$ of $\sf{\dfrac{3}{4}}$

➜ New Share of Suresh = $\sf{\dfrac{5}{8}}$ × $\sf{\dfrac{3}{4}}$

➜ New Share of Suresh = $\sf{\dfrac{15}{32}}$

And,

• ⍟ New Share of Ramesh = $\sf{\dfrac{3}{8}}$ of $\sf{\dfrac{3}{4}}$

➜ New Share of Ramesh = $\sf{\dfrac{3}{8}}$ × $\sf{\dfrac{3}{4}}$

➜ New Share of Ramesh = $\sf{\dfrac{9}{32}}$

Also,

• ⍟ Share of Deepak = $\sf{\dfrac{1}{4}}$

➜ Share of Deepak = $\sf{\dfrac{1 \times 8}{4 \times 8}}$

➜ Share of Deepak = $\sf{\dfrac{8}{32}}$

Thus,

• ✫ Profit Sharing Ratio of Suresh, Ramesh and Deepak = New Share of Suresh : New Share of Ramesh : Share of Deepak

➝ Profit Sharing Ratio of Suresh, Ramesh and Deepak = $\sf{\dfrac{15}{32}}$ : $\sf{\dfrac{9}{32}}$ : $\sf{\dfrac{8}{32}}$

➝ Profit Sharing Ratio of Suresh, Ramesh and Deepak = 15 : 9 : 8

Again,

• Karan was admitted as a new partner for $\sf{\dfrac{1}{6}}$ th share of profit on 31st July, 2018.

• Karan acquired his share equally from Suresh, Ramesh and Deepak.

So,

• ✠ Karan acquired share from Suresh = $\sf{\dfrac{1}{3}}$ of $\sf{\dfrac{1}{6}}$

⟾ Karan acquired share from Suresh = $\sf{\dfrac{1}{3}}$ × $\sf{\dfrac{1}{6}}$

⟾ Karan acquired Share from Suresh = $\sf{\dfrac{1}{18}}$

Similarly,

• ✠ Karan acquired share from Ramesh = $\sf{\dfrac{1}{18}}$

And,

• ✠ Karan acquired share from Deepak = $\sf{\dfrac{1}{18}}$

So,

• ❍ Karan's Share = Share acquires from Suresh + Share acquires from Ramesh + Share acquires from Deepak

➜ Karan's Share = $\sf{\dfrac{1}{18}}$ + $\sf{\dfrac{1}{18}}$ + $\sf{\dfrac{1}{18}}$

➜ Karan's Share = $\sf{\dfrac{3}{18}}$

Also,

• Profit Sharing Ratio of Suresh, Ramesh and Deepak = 15 : 9 : 8.

So,

• Old Share of Suresh = $\sf{\dfrac{15}{32}}$

• Old Share of Ramesh = $\sf{\dfrac{9}{32}}$

• Old Share of Deepak = $\sf{\dfrac{8}{32}}$

Also,

• Share Sacrificed by Suresh = $\sf{\dfrac{1}{18}}$

• Share Sacrificed by Ramesh = $\sf{\dfrac{1}{18}}$

• Share Sacrificed by Deepak = $\sf{\dfrac{1}{18}}$

Therefore,

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

➨ Suresh's New Share = $\sf{\dfrac{15}{32}}$ - $\sf{\dfrac{1}{18}}$

➨ Suresh's New Share = $\sf{\dfrac{119}{288}}$

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

➨ Ramesh's New Share = $\sf{\dfrac{9}{32}}$ - $\sf{\dfrac{1}{18}}$

➨ Ramesh's New Share = $\sf{\dfrac{65}{288}}$

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

➨ Deepam's New Share = $\sf{\dfrac{8}{32}}$ - $\sf{\dfrac{1}{18}}$

➨ Deepak's New Share = $\sf{\dfrac{56}{288}}$

And,

• ★ Share of Karan = $\sf{\dfrac{3}{18}}$

➨ Share of Karan = $\sf{\dfrac{3 \times 16}{18 \times 16}}$

➨ Share of Karan = $\sf{\dfrac{48}{288}}$

Hence,

• ✪ New Profit Sharing Ratio of Suresh, Ramesh, Deepak and Karan = New Share of Suresh : New Share of Ramesh : New Share of Deepak : Share of Karan

⇒ New Profit Sharing Ratio of Suresh, Ramesh, Deepak and Karan = $\sf{\dfrac{119}{288}}$ : $\sf{\dfrac{65}{288}}$ : $\sf{\dfrac{56}{288}}$ : $\sf{\dfrac{48}{288}}$

∴ New Profit Sharing Ratio of Suresh, Ramesh, Deepak and Karan = 119 : 65 : 56 : 48