Question

A,B& C are partners sharing profits 5:3:2. D is admitted for 3/10th share in pofit which he acquires from A B & ratio of 2:2:1. Calculate N,R,​

Answer 1

Given data:

• A, B and C are partners sharing profits and losses in the ratio 5:3:2.
• D is admitted into the firm for 3/10th share of profits and losses, which he acquires from A, B and C in the ratio 2:2:1.

To find: The new profit-sharing ratio.

Answer:

D acquires 3/10th share from A, B and C in the ratio 2:2:1. Therefore, D's share will be equivalent to the sum of 3/10 deducted from each partner's ratio [2:2:1.]

From A:

• 2/5 of 3/10 = 6/50

From B:

• 2/5 of 3/10 = 6/50

From C:

• 1/5 of 3/10 = 3/50

Therefore, D's share of profit = 6/50 + 6/50 + 3/50 = 15/50.

The new profit sharing ratio of the others = Old share profit - Share profit surrendered.

For A:

• 5/10 - 6/50 = (25 - 6)/50 = 19/50

For B:

• 3/10 - 6/50 = (15 - 6)/50 = 9/50

For C:

• 2/10 - 3/50 = (10 - 3)/50 = 7/50

For D:

• As calculated above, 15/50

Therefore, the new profit sharing ratio is 19:9:7:15.

Answer 2

ANSWER :

• ❖ If A, B and C are partners sharing profits 5 : 3 : 2 and D is admitted for 3/10th share in pofit which he acquires from A, B and C ratio of 2 : 2 : 1; then New Profit Sharing Ratio of A, B, C and D will be 19 : 9 : 7 : 15.

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SOLUTION :

❒ Given :-

• A, B and C are partners sharing profits 5 : 3 : 2.

• D is admitted as partner with $\sf{\dfrac{3}{10}}$ th share in profit.

• D takes his share from A, B and C in the ratio of 2 : 2 : 1.

❒ To Calculate :-

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

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❒ Calculation :-

It is given that,

• D is admitted as partner with $\sf{\dfrac{3}{10}}$ th share in profit.

• D takes his share from A, B and C in the ratio of 2 : 2 : 1.

So,

• ✠ D acquires share of profit from A = $\sf{\dfrac{2}{5}}$ th of $\sf{\dfrac{3}{10}}$

⇒ D acquires share of profit from A = $\sf{\dfrac{2}{5}}$ × $\sf{\dfrac{3}{10}}$

⇒ D acquires share of profit from A = $\sf{\dfrac{6}{50}}$

Also,

• ✠ D acquires share of profit from B = $\sf{\dfrac{2}{5}}$ th of $\sf{\dfrac{3}{10}}$

⇒ D acquires share of profit from B = $\sf{\dfrac{2}{5}}$ × $\sf{\dfrac{3}{10}}$

⇒ D acquires share of profit from B = $\sf{\dfrac{6}{50}}$

And,

• ✠ D acquires share of profit from C = $\sf{\dfrac{1}{5}}$ th of $\sf{\dfrac{3}{10}}$

⇒ D acquires share of profit from C = $\sf{\dfrac{1}{5}}$ × $\sf{\dfrac{3}{10}}$

⇒ D acquires share of profit from C = $\sf{\dfrac{3}{50}}$

Thus,

• ❍ Share of D = D acquires share of profit from A + D acquires share of profit from B + D acquires share of profit from C

⇒ Share of D = $\sf{\dfrac{6}{50}}$ + $\sf{\dfrac{6}{50}}$ + $\sf{\dfrac{3}{50}}$

⇒ Share of D = $\sf{\dfrac{6 + 6 + 3}{50}}$

⇒ Share of D = $\sf{\dfrac{15}{50}}$

Again,

• Old Profit Sharing Ratio between A, B and C is 5 : 3 : 2

So,

• A's Old Share = $\sf{\dfrac{5}{10}}$

• B's Old Share = $\sf{\dfrac{3}{10}}$

• C's Old Share = $\sf{\dfrac{2}{10}}$

However,

• Share surrendered by A = $\sf{\dfrac{6}{50}}$

• Share surrendered by B = $\sf{\dfrac{6}{50}}$

• Share surrendered by C = $\sf{\dfrac{3}{50}}$

We know that,

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

Using this formula, we get,

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

➨ A's New Share = $\sf{\dfrac{5}{10}}$ - $\sf{\dfrac{6}{50}}$

➨ A's New Share = $\sf{\dfrac{25 - 6}{50}}$

➨ A's New Share = $\sf{\dfrac{19}{50}}$

And,

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

➨ B's New Share = $\sf{\dfrac{3}{10}}$ - $\sf{\dfrac{6}{50}}$

➨ B's New Share = $\sf{\dfrac{15 - 6}{50}}$

➨ B's New Share = $\sf{\dfrac{9}{50}}$

And,

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

➨ C's New Share = $\sf{\dfrac{2}{10}}$ - $\sf{\dfrac{3}{50}}$

➨ C's New Share = $\sf{\dfrac{10 - 3}{50}}$

➨ C's New Share = $\sf{\dfrac{7}{50}}$

Also,

• ★ Share of D = $\sf{\dfrac{15}{50}}$

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 = $\sf{\dfrac{19}{50}}$ : $\sf{\dfrac{9}{50}}$ : $\sf{\dfrac{7}{50}}$ : $\sf{\dfrac{15}{50}}$

∴ New Profit Sharing Ratio of A, B, C and D = 19 : 9 : 7 : 15