Question

QUESTION:-

A , B,C and D are partners sharing progits in the ratio of 4:3:2:1 . they admitted E as a new partner for 1/10th share. It is agreed that C and D will retain their original shares. what will be the new profit sharing ratio?​

Answer 1

Given : A ,B, C and D are partners sharing progits in the ratio of 4:3:2:1. they admitted E as a new partner for 1/10th share. It is agreed that C and D will retain their original shares.

To Find : Find the new profite sharing ratio ?

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Solution : Let the new profite sharing ratio be x.

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Old ratios :

• A : B : C : D
• 4 : 3 : 2 : 1

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$\qquad{\sf\dashrightarrow{A's~Share~=~\pmb{\dfrac{4}{10}}}}$

$\qquad{\sf\dashrightarrow{B's~Share~=~\pmb{\dfrac{3}{10}}}}$

$\qquad{\sf\dashrightarrow{C's~Share~=~\pmb{\dfrac{2}{10}}}}$

$\qquad{\sf\dashrightarrow{D's~Share~=~\pmb{\dfrac{1}{10}}}}$

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They admit E as a new partner for 1/10th Share.

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• E's Share = 1/10

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C and D will retain their original share.

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• Total Share = 1

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Balance of Share remain A and B

$\qquad{\sf:\implies{\dfrac{1~-~4}{10}~=~\pmb{\dfrac{6}{10}}}}$

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• Remaining Share divided into A and B in their old ratio 4 : 3.

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New Profit Sharing Ratio :

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• A's new Share

$\qquad{\sf:\implies{\dfrac{4}{7}~×~\dfrac{6}{10}~=~\pmb{\dfrac{24}{70}}}}$

• B's new Share

$\qquad{\sf:\implies{\dfrac{3}{7}~×~\dfrac{6}{10}~=~\pmb{\dfrac{18}{70}}}}$

• C's new Share

$\qquad{\sf:\implies{\dfrac{2}{10}~×~\dfrac{7}{7}~=~\pmb{\dfrac{14}{70}}}}$

• D's new Share

$\qquad{\sf:\implies{\dfrac{1}{10}~×~\dfrac{7}{7}~=~\pmb{\dfrac{7}{70}}}}$

• E's new Share

$\qquad{\sf:\implies{\dfrac{1}{10}~×~\dfrac{7}{7}~=~\pmb{\dfrac{7}{70}}}}$

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New Profit Sharing Ratio :

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$\qquad{\sf:\implies{A's~ratio~=~\pmb{\dfrac{24}{70}}}}$

$\qquad{\sf:\implies{B's~ratio~=~\pmb{\dfrac{18}{70}}}}$

$\qquad{\sf:\implies{C's~ratio~=~\pmb{\dfrac{14}{70}}}}$

$\qquad{\sf:\implies{D's~ratio~=~\pmb{\dfrac{7}{70}}}}$

$\qquad{\sf:\implies{E's~ratio~=~\pmb{\dfrac{7}{70}}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{24~:~18~:~14~:~7~:~7}}}}}}$★

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Hence,

• The new sharing ratio of A, B, C, D and E is 24 : 18 : 14 : 7 : 7.

Answer 2

Answer:

The total profit sharing ratio of A, B, C, and D is 4+3+2+1 = 10.

Let X be the total profit share, then the profit shares of A, B, C, and D are 4X/10, 3X/10, 2X/10, and 1X/10, respectively.

Now, E is admitted for 1/10th share, which is (1/10)X.

Since C and D will retain their original shares, the remaining profit share is 10X/10 - 2X/10 - 1X/10 = 7X/10.

So, the new profit sharing ratio will be:

A = 4X/10 + (1/10)X = 5X/10

B = 3X/10 + (1/10)X = 4X/10

C = 2X/10

D = 1X/10

E = 1X/10

Simplifying the ratios by dividing by 1/10, we get:

A:B:C:D:E = 50:40:20:10:10

Therefore, the new profit sharing ratio of A, B, C, D, and E is 50:40:20:10:10.