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

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 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 :

    [tex] \\ [/tex]

    • ➤ 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 :

    [tex] \\ [/tex]

    • ❖ 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 :

    [tex] \\ \\ [/tex]

    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 :-

    [tex] \\ [/tex]

    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]

    [tex] \\ [/tex]

    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]

    [tex] \\ [/tex]

    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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