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

1 thought on “Ans. New ratio 94:53<br />& X and Y are partners in a firm sharing profits in the ratio of 2:1. Zom<br />the firm X surrenders”

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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   ANSWER :

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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 = [tex]\sf{\dfrac{2}{3}}[/tex]

   • Old share of Y = [tex]\sf{\dfrac{1}{3}}[/tex]

   Again,

   • On admission of Z, X surrenders [tex]\sf{\dfrac{1}{4}}[/tex] th of his share.

   Thus,

   • ✠ Share surrendered by X = [tex]\sf{\dfrac{1}{4}}[/tex] th of [tex]\sf{\dfrac{2}{3}}[/tex]

   ➜ Share surrendered by X = [tex]\sf{\dfrac{1}{4}}[/tex] × [tex]\sf{\dfrac{2}{3}}[/tex]

   ➜ Share surrendered by X = [tex]\sf{\dfrac{2}{12}}[/tex]

   And,

   • On admission of Z, Y surrenders [tex]\sf{\dfrac{1}{5}}[/tex] th of his share.

   Thus,

   • ✠ Share surrendered by Y = [tex]\sf{\dfrac{1}{5}}[/tex] th of [tex]\sf{\dfrac{1}{3}}[/tex]

   ➜ Share surrendered by Y = [tex]\sf{\dfrac{1}{5}}[/tex] × [tex]\sf{\dfrac{1}{3}}[/tex]

   ➜ Share surrendered by Y = [tex]\sf{\dfrac{1}{15}}[/tex]

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   We know that,

   • [tex] \dag \: \: \underline{ \boxed{ \sf{ \: New \: \: Share = Old \: \: Share – Share \: \: Surrendered \: }}}[/tex]

   [tex] \\ [/tex]

   Using this formula,

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

   ⇒ New Share of X = [tex]\sf{\dfrac{2}{3}}[/tex] – [tex]\sf{\dfrac{2}{12}}[/tex]

   ⇒New Share of X = [tex]\sf{\dfrac{8 – 2}{12}}[/tex]

   ⇒New Share of X = [tex]\sf{\dfrac{6}{12}}[/tex]

   ⇒ New Share of X = [tex]\sf{\dfrac{6 \times 5}{12 \times 5}}[/tex]

   ∴ New Share of X = [tex]\sf{\dfrac{30}{60}}[/tex]

   Also,

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

   ⇒ New Share of Y = [tex]\sf{\dfrac{1}{3}}[/tex] – [tex]\sf{\dfrac{1}{15}}[/tex]

   ⇒ New Share of Y = [tex]\sf{\dfrac{5 – 1}{15}}[/tex]

   ⇒ New Share of Y = [tex]\sf{\dfrac{4}{15}}[/tex]

   ⇒ New Share of Y = [tex]\sf{\dfrac{4 \times 4}{15 \times 4}}[/tex]

   ∴ New Share of Y = [tex]\sf{\dfrac{16}{60}}[/tex]

   And,

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

   ⇒ Share of Z = [tex]\sf{\dfrac{2}{12}}[/tex] + [tex]\sf{\dfrac{1}{15}}[/tex]

   ⇒ Share of Z = [tex]\sf{\dfrac{10 + 4}{60}}[/tex]

   ∴ Share of Z = [tex]\sf{\dfrac{14}{60}}[/tex]

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   Therefore,

   • ✪ New Profit Sharing Ratio among X, Y and Z = [tex]\sf{\dfrac{30}{60}}[/tex] : [tex]\sf{\dfrac{16}{60}}[/tex] : [tex]\sf{\dfrac{14}{60}}[/tex]

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

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

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