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

# Ans. New ratio 94:53

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CORRECT QUESTION :[tex] \\ [/tex]

___________________________________________________________ANSWER :[tex] \\ [/tex]

New Profit Sharing Ratio among X, Y and Zis.15 : 8 : 7___________________________________________________________SOLUTION :[tex] \\ \\ [/tex]

## ❒

Given :-## ❒

To Find :-____________________________________________

## ❒

Calculation :-[tex] \\ [/tex]

It is given that,Thus,

Again,Thus,

➜ 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,Thus,

➜ 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] \\ [/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