Question

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​

Answer 1

CORRECT QUESTION :

• ➤ 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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ANSWER :

• ❖ 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 :

❒ 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 :-

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 = $\sf{\dfrac{1}{15}}$

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 = $\sf{\dfrac{2}{3}}$ - $\sf{\dfrac{2}{12}}$

⇒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 = $\sf{\dfrac{14}{60}}$

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

∴ New Profit Sharing Ratio among X, Y and Z = 15 : 8 : 7