Question

U and V were partners sharing profits and losses in the ratio of 3:2. D was admitted for 1/4"" share which he takes from U and Vin the ratio of 2:1. calculate new ratio and sacrificing ratio. 2 marks​

Answer 1

ANSWER :

• ❖ If U and V are partners in a firm sharing profits and losses in the ratio of 3 : 2 and D is admitted as partner with 1/4 share in profit which he takes from U and V in the ratio of 2 : 1; then the New Profit Sharing Ratio among U, V and D will be 26 : 19 : 15 and Sacrificing Ratio between U and V will be 2 : 1.

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SOLUTION :

❒ Given :-

• U and V are partners in a firm sharing profits and losses in the ratio of 3 : 2.

• D is admitted as partner with $\sf{\dfrac{1}{4}}$ share in profit.

• D takes his share from U and V in the ratio of 2 : 1.

❒ To Calculate :-

• New Profit Sharing Ratio among U, V and D = ?

• Sacrificing Ratio between U and V = ?

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❒ Calculation of New Profit Sharing Ratio :-

It is given that,

• D is admitted as partner with $\sf{\dfrac{1}{4}}$ share in profit.

• D takes his share from U and V in the ratio of 2 : 1.

So,

• ✠ D acquires share of profit from U = $\sf{\dfrac{2}{3}}$ th of $\sf{\dfrac{1}{4}}$

⇒ D acquires share of profit from U = $\sf{\dfrac{2}{3}}$ × $\sf{\dfrac{1}{4}}$

⇒ D acquires share of profit from U = $\sf{\dfrac{2}{12}}$

And,

• ✠ D acquires share of profit from V = $\sf{\dfrac{1}{3}}$th of $\sf{\dfrac{1}{4}}$

⇒ D acquires share of profit from V = $\sf{\dfrac{1}{3}}$ × $\sf{\dfrac{1}{4}}$

⇒ D acquires share of profit from V = $\sf{\dfrac{1}{12}}$

Thus,

• ❍ Share of D = D acquires share of profit from U + D acquires share of profit from V

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

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

⇒ Share of D = $\sf{\dfrac{3}{12}}$

Again,

• Old Profit Sharing Ratio between U and V is 3 : 2

So,

• U's Old Share = $\sf{\dfrac{3}{5}}$

• V's Old Share = $\sf{\dfrac{2}{5}}$

Also,

• Share surrendered by U = $\sf{\dfrac{2}{12}}$

• Share surrendered by V = $\sf{\dfrac{1}{12}}$

We know that,

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

Using this formula, we get,

• ★ U's New Share = U's Old Share - Share surrendered by U

➨ U's New Share = $\sf{\dfrac{3}{5}}$ - $\sf{\dfrac{2}{12}}$

➨ U's New Share = $\sf{\dfrac{36 - 10}{60}}$

➨ U's New Share = $\sf{\dfrac{26}{60}}$

And,

• ★ V's New Share = V's Old Share - Share surrendered by V

➨ V's New Share = $\sf{\dfrac{2}{5}}$ - $\sf{\dfrac{1}{12}}$

➨ V's New Share = $\sf{\dfrac{24 - 5}{60}}$

➨ V's New Share = $\sf{\dfrac{19}{60}}$

And,

• ★ Share of D = $\sf{\dfrac{3}{12}}$

➨ Share of D = $\sf{\dfrac{3 \times 5}{12 \times 5}}$

➨ Share of D = $\sf{\dfrac{15}{60}}$

Hence,

• ✪ New Profit Sharing Ratio of U, V and D = New Share of U : New Share of V : Share of D

⇒ New Profit Sharing Ratio of U, V and D = $\sf{\dfrac{26}{60}}$ : $\sf{\dfrac{19}{60}}$ : $\sf{\dfrac{15}{60}}$

∴ New Profit Sharing Ratio of U, V and D = 26 : 19 : 15

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❒ Calculation of Sacrificing Ratio :-

Here,

• Old Profit Sharing Ratio of U and V = 3 : 2

So,

• Old Share of U = $\sf{\dfrac{3}{5}}$

• Old Share of V = $\sf{\dfrac{2}{5}}$

And,

• New Profit Sharing Ratio of U, V and D = 26 : 19 : 15

So,

• New Share of U = $\sf{\dfrac{26}{60}}$

• New Share of V = $\sf{\dfrac{19}{60}}$

We know that,

• $\dag \: \: \underline{ \boxed{ \bold{ \: Sacrifice = Old \: \: Share - New \: \: Share \: }}}$

Using this formula, we get,

• ★ Sacrifice of U = Old Share of U - New Share of U

➨ Sacrifice of U = $\sf{\dfrac{3}{5}}$ - $\sf{\dfrac{26}{60}}$

➨ Sacrifice of U = $\sf{\dfrac{36 - 26}{60}}$

➨ Sacrifice of U = $\sf{\dfrac{10}{60}}$

And,

• ★ Sacrifice of V = Old Share of V - New Share of V

➨ Sacrifice of V = $\sf{\dfrac{2}{5}}$ - $\sf{\dfrac{19}{60}}$

➨ Sacrifice of V = $\sf{\dfrac{24 - 19}{60}}$

➨ Sacrifice of V = $\sf{\dfrac{5}{60}}$

Hence,

• ✪ Sacrificing Ratio of U and V = Sacrifice of U : Sacrifice of V

⇒ Sacrificing Ratio of U and V = $\sf{\dfrac{10}{60}}$ : $\sf{\dfrac{5}{60}}$

⇒ Sacrificing Ratio of U and V = 10 : 5

∴ Sacrificing Ratio of U and V = 2 : 1