Question

, Y and Z are partners sharing profits in the ratio of 5:3:2. Calculate new profit sharing ratio if Z acquires 1/5th share of X and 1/6th share of Y​

Answer 1

CORRECT QUESTION :

• ➲ X, Y and Z are partners sharing profits in the ratio of 5 : 3 : 2. Calculate new profit sharing ratio, if Z acquires 1/5 th share of X and 1/6 th share of Y.

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ANSWER :

• ❖ If X, Y and Z are partners sharing profits in the ratio of 5 : 3 : 2 and Z acquires 1/5 th share of X and 1/6 th share of Y, then new profit sharing ratio will be 8 : 5 : 7.

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SOLUTION :

❒ Given :-

• Old Profit Sharing Ratio of X, Y and Z = 5 : 3 : 2

• Z acquires 1/5 th share of X and 1/6 th share of Y

❒ To Calculate :-

• New Profit Sharing Ratio of X, Y and Z = ?

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❒ Calculation :-

We have,

• Old Profit Sharing Ratio of X, Y and Z = 5 : 3 : 2

Therefore,

• Old share of X = $\sf{\dfrac{5}{10}}$

• Old share of Y = $\sf{\dfrac{3}{10}}$

• Old share of Z = $\sf{\dfrac{2}{10}}$

Again,

• Z acquired $\sf{\frac{1}{5}}$ th share from X.

∴ Share acquired by Z from X = $\sf{\dfrac{1}{5}}$ th of $\sf{\dfrac{5}{10}}$

⇒ Share acquired by Z from X = $\sf{\dfrac{1}{5}}$ × $\sf{\dfrac{5}{10}}$

⇒ Share acquired by Z from X = $\sf{\dfrac{1}{10}}$

And,

• Z acquired $\sf{\frac{1}{6}}$ th share from Y.

∴ Share acquired by Z from Y = $\sf{\dfrac{1}{6}}$ th of $\sf{\dfrac{3}{10}}$

⇒ Share acquired by Z from Y = $\sf{\dfrac{1}{6}}$ × $\sf{\dfrac{3}{10}}$

⇒ Share acquired by Z from Y = $\sf{\dfrac{1}{20}}$

• ∴ Total share acquired by Z = Share acquired by Z from X + Share acquired by Z from Y

➨ Total share acquired by Z = $\sf{\dfrac{1}{10}}$ + $\sf{\dfrac{1}{20}}$

➨ Total share acquired by Z = $\sf{\dfrac{2}{20}}$ + $\sf{\dfrac{1}{20}}$

➨ Total share acquired by Z = $\sf{\dfrac{2 + 1}{20}}$

➨ Total share acquired by Z = $\sf{\dfrac{3}{20}}$

Now,

• ★ New Share of X = Old Share - Share acquired by Z

➜ New Share of X = $\sf{\dfrac{5}{10}}$ - $\sf{\dfrac{1}{10}}$

➜ New Share of X = $\sf{\dfrac{5 - 1}{10}}$

➜ New Share of X = $\sf{\dfrac{4}{10}}$

∴ New Share of X = $\sf{\dfrac{8}{20}}$

And,

• ★ New Share of Y = Old Share - Share acquired by Z

➜ New Share of Y = $\sf{\dfrac{3}{10}}$ - $\sf{\dfrac{1}{20}}$

➜ New Share of Y = $\sf{\dfrac{6}{20}}$ - $\sf{\dfrac{1}{20}}$

➜ New Share of Y = $\sf{\dfrac{6 - 1}{20}}$

∴ New Share of Y = $\sf{\dfrac{5}{20}}$

And,

• ★ New Share of Z = Old Share + Share acquired from X and Y

➜ New Share of Z = $\sf{\dfrac{2}{10}}$ + $\sf{\dfrac{3}{20}}$

➜ New Share of Z = $\sf{\dfrac{4}{20}}$ + $\sf{\dfrac{3}{20}}$

➜ New Share of Z = $\sf{\dfrac{4 + 3}{20}}$

∴ New Share of Z = $\sf{\dfrac{7}{20}}$

Hence,

• ✪ New Profit Sharing Ratio = $\sf{\dfrac{8}{20}}$ : $\sf{\dfrac{5}{20}}$ : $\sf{\dfrac{7}{20}}$

∴ New Profit Sharing Ratio = 8 : 5 : 7