Question

X and Y shared profits in the ratio of 7:3 . Z is admitted as a partner X surrended 1/7th of his share and Y 1/3 th of his share in favour of Z. calculate the new profit sharing ratio.
answer________new profit sharing ratio X:Y:Z = 3:1:1​

Answer 1

Answer:

Explanation:

Correct option is

B

6 : 2 : 2

A and B are partners in a firm sharing profit/losses in the ratio 7 : 3.

A will surrender 1/7th of his share for C = 7/10 *3/21

                                                                 = 21/210

B will surrender 1/3rd of his share for C = 3/10 * 7/21

                                                                 = 21/210

Now , the new profit sharing ratio of A,B and C will be :

A=  7/10 - 21/210 = 126/210

B=  3/10 - 21/210 = 42/210

C= 21/210 + 21/210 = 42/210

Hence , 146 : 42 : 42 can be written as 6 : 2 : 2

Answer 2

ANSWER :

• ❖ If X and Y are partners sharing profits in the ratio of 7 : 3 and when Z is admitted, X surrenders 1/7 th of his share and Y surrenders 1/3 rd of his share in favour of Z; then the New Profit Sharing Ratio of X, Y and Z will be 3 : 1 : 1.

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SOLUTION :

❒ Given :-

• X and Y are partners in a firm sharing profits in the ratio of 7 : 3.

• When Z is admitted to the firm, X surrenders 1/7th of his share and Y surrenders 1/3rd of his shares in favour of Z.

❒ To Find :-

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

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❒ Calculation :-

It is given that,

• Old profit sharing ratio between X and Y = 7 : 3

So,

• Old share of X = $\sf{\dfrac{7}{10}}$

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

Again,

• On admission of Z, X surrenders $\sf{\dfrac{1}{7}}$ th of his shares.

Thus,

• ✠ Share surrendered by X = $\sf{\dfrac{1}{7} \: \:  of \: \: \dfrac{7}{10}}$

➜ Share surrendered by X = $\sf{\dfrac{1}{7} \times \dfrac{7}{10}}$

➜ Share surrendered by X = $\sf{\dfrac{1}{10}}$

And,

• On admission of Z, Y surrenders $\sf{\dfrac{1}{3}}$ rd of his share.

Thus,

• ✠ Share surrendered by Y = $\sf{\dfrac{1}{3} \: \:  of \: \: \dfrac{3}{10}}$

➜ Share surrendered by Y = $\sf{\dfrac{1}{3} \times \dfrac{3}{10}}$

➜ Share surrendered by Y = $\sf{\dfrac{1}{10}}$

We know that,

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

Using this formula,

• ★ New Share of X = Old Share of X - Share Surrendered by X

⇒ New Share of X = $\tt{\dfrac{7}{10} - \dfrac{1}{10}}$

⇒New Share of X = $\tt{\dfrac{7 - 1}{10}}$

⇒ New Share of X = $\tt{\dfrac{6}{10}}$

Similarly,

• ★ New Share of Y = Old Share of Y - Share Surrendered by Y

⇒ New Share of Y = $\tt{\dfrac{3}{10} - \dfrac{1}{10}}$

⇒New Share of Y = $\tt{\dfrac{3 - 1}{10}}$

⇒ New Share of Y = $\tt{\dfrac{2}{10}}$

And,

• ★ Share of Z = Share Surrendered by X + Share Surrendered by Y

⇒ Share of Z = $\tt{\dfrac{1}{10} + \dfrac{1}{10}}$

⇒ Share of Z = $\tt{\dfrac{1 + 1}{10}}$

⇒ Share of Z = $\tt{\dfrac{2}{10}}$

Therefore,

• ✪ New Profit Sharing Ratio of X, Y and Z = New Share of X : New Share of Y : Share of Z

➨ New Profit Sharing Ratio of X, Y and Z = $\tt{\dfrac{6}{10}}$ : $\tt{\dfrac{2}{10}}$ : $\tt{\dfrac{2}{10}}$

➨ New Profit Sharing Ratio of X, Y and X = 6 : 2 : 2

∴ New Profit Sharing Ratio among X, Y and Z = 3 : 1 : 1