# Ans. New ratio 94:53& X and Y are partners in a firm sharing profits in the ratio of 2:1. Zomthe firm X surrenders

Ans. New ratio 94:53
& X and Y are partners in a firm sharing profits in the ratio of 2:1. Zom
the firm X surrenders 14th of his share and Y 1/5th of his shares
favour of Z. Find new profit sharing ratio.
(C.B.S.E., 2004
Ans. 15:8​

1. ## CORRECT QUESTION :

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• ➤ X and Y are partners in a firm sharing profits in the ratio of 2 : 1. Z is admitted to the firm. For this, X surrenders 1/4th of his share and Y surrenders 1/5th of his shares in favour of Z. Find the new profit sharing ratio.

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• ❖ If X and Y are partners in a firm sharing profits in the ratio of 2 : 1 and Z is admitted to the firm, for which X surrenders 1/4th of his share and Y surrenders 1/5th of his shares in favour of Z; then the New Profit Sharing Ratio among X, Y and Z is 15 : 8 : 7.

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## SOLUTION :

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### ❒ Given :-

• X and Y are partners in a firm sharing profits in the ratio of 2 : 1.
• When Z is admitted to the firm, X surrenders 1/4th of his share and Y surrenders 1/5th of his shares in favour of Z.

### ❒ To Find :-

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

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### ❒ Calculation :-

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It is given that,

• Old profit sharing ratio between X and Y = 2 : 1.

Thus,

• Old share of X = $$\sf{\dfrac{2}{3}}$$
• Old share of Y = $$\sf{\dfrac{1}{3}}$$

Again,

• On admission of Z, X surrenders $$\sf{\dfrac{1}{4}}$$ th of his share.

Thus,

• ✠ Share surrendered by X = $$\sf{\dfrac{1}{4}}$$ th of $$\sf{\dfrac{2}{3}}$$

➜ Share surrendered by X = $$\sf{\dfrac{1}{4}}$$ × $$\sf{\dfrac{2}{3}}$$

➜ Share surrendered by X = $$\sf{\dfrac{2}{12}}$$

And,

• On admission of Z, Y surrenders $$\sf{\dfrac{1}{5}}$$ th of his share.

Thus,

• ✠ Share surrendered by Y = $$\sf{\dfrac{1}{5}}$$ th of $$\sf{\dfrac{1}{3}}$$

➜ Share surrendered by Y = $$\sf{\dfrac{1}{5}}$$ × $$\sf{\dfrac{1}{3}}$$

➜ Share surrendered by Y = $$\sf{\dfrac{1}{15}}$$

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We know that,

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

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Using this formula,

• New Share of X = Old Share of X – Share Surrendered by X

⇒ New Share of X = $$\sf{\dfrac{2}{3}}$$ – $$\sf{\dfrac{2}{12}}$$

⇒New Share of X = $$\sf{\dfrac{8 – 2}{12}}$$

⇒New Share of X = $$\sf{\dfrac{6}{12}}$$

⇒ New Share of X = $$\sf{\dfrac{6 \times 5}{12 \times 5}}$$

New Share of X = $$\sf{\dfrac{30}{60}}$$

Also,

• New Share of Y = Old Share of Y – Share Surrendered by Y

⇒ New Share of Y = $$\sf{\dfrac{1}{3}}$$ – $$\sf{\dfrac{1}{15}}$$

⇒ New Share of Y = $$\sf{\dfrac{5 – 1}{15}}$$

⇒ New Share of Y = $$\sf{\dfrac{4}{15}}$$

⇒ New Share of Y = $$\sf{\dfrac{4 \times 4}{15 \times 4}}$$

New Share of Y = $$\sf{\dfrac{16}{60}}$$

And,

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

⇒ Share of Z = $$\sf{\dfrac{2}{12}}$$ + $$\sf{\dfrac{1}{15}}$$

⇒ Share of Z = $$\sf{\dfrac{10 + 4}{60}}$$

Share of Z = $$\sf{\dfrac{14}{60}}$$

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Therefore,

• New Profit Sharing Ratio among X, Y and Z = $$\sf{\dfrac{30}{60}}$$ : $$\sf{\dfrac{16}{60}}$$ : $$\sf{\dfrac{14}{60}}$$

➨ New Profit Sharing Ratio among X, Y and Z = 30 : 16 : 14