Question

P and Q are partners sharing profits in 2:1 ratio. They admitted R into partnership giving him 1/5 share which he acquired from P and 9 in 1:2 ratio. Calculate new profit sharing ratio?​

Answer 1

ANSWER :

• ❖ If P and Q are partners in a firm sharing profits and losses in the ratio of 2 : 1 and R is admitted as partner with 1/5 share in profit which he takes from U and V in the ratio of 1 : 2; then the New Profit Sharing Ratio among P, Q and R will be 3 : 1 : 1.

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SOLUTION :

❒ Given :-

• P and Q are partners in a firm sharing profits and losses in the ratio of 2 : 1.

• R is admitted as partner with $\sf{\dfrac{1}{5}}$ share in profit.

• R takes his share from P and Q in the ratio of 1 : 2.

❒ To Calculate :-

• New Profit Sharing Ratio among P, Q and R = ?

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❒ Calculation :-

It is given that,

• R is admitted as partner with $\sf{\dfrac{1}{5}}$ share in profit.

• R takes his share from P and Q in the ratio of 1 : 2.

So,

• ✠ R acquires share of profit from P = $\sf{\dfrac{1}{3}}$ th of $\sf{\dfrac{1}{5}}$

⇒ R acquires share of profit from P = $\sf{\dfrac{1}{3}}$ × $\sf{\dfrac{1}{5}}$

⇒ R acquires share of profit from P = $\sf{\dfrac{1}{15}}$

And,

• ✠ R acquires share of profit from Q = $\sf{\dfrac{2}{3}}$ th of $\sf{\dfrac{1}{5}}$

⇒ R acquires share of profit from Q = $\sf{\dfrac{2}{3}}$ × $\sf{\dfrac{1}{5}}$

⇒ R acquires share of profit from Q = $\sf{\dfrac{2}{15}}$

Thus,

• ❍ Share of R = R acquires share of profit from P + R acquires share of profit from Q

⇒ Share of R = $\sf{\dfrac{1}{15}}$ + $\sf{\dfrac{2}{15}}$

⇒ Share of R = $\sf{\dfrac{1 + 2}{15}}$

⇒ Share of R = $\sf{\dfrac{3}{15}}$

Again,

• Old Profit Sharing Ratio between P and Q is 2 : 1.

So,

• P's Old Share = $\sf{\dfrac{2}{3}}$

• Q's Old Share = $\sf{\dfrac{1}{3}}$

Also,

• Share surrendered by P = $\sf{\dfrac{1}{15}}$

• Share surrendered by Q = $\sf{\dfrac{2}{15}}$

We know that,

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

Using this formula, we get,

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

➨ P's New Share = $\sf{\dfrac{2}{3}}$ - $\sf{\dfrac{1}{15}}$

➨ P's New Share = $\sf{\dfrac{10 - 1}{15}}$

➨ P's New Share = $\sf{\dfrac{9}{15}}$

➨ P's New Share = $\sf{\dfrac{3}{5}}$

And,

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

➨ Q's New Share = $\sf{\dfrac{1}{3}}$ - $\sf{\dfrac{2}{15}}$

➨ Q's New Share = $\sf{\dfrac{5 - 2}{15}}$

➨ Q's New Share = $\sf{\dfrac{3}{15}}$

➨ Q's New Share = $\sf{\dfrac{1}{5}}$

And,

• ★ Share of R = $\sf{\dfrac{3}{15}}$

➨ Share of R = $\sf{\dfrac{1}{5}}$

Hence,

• ✪ New Profit Sharing Ratio of P, Q and R = New Share of P : New Share of Q : Share of R

⇒ New Profit Sharing Ratio of P, Q and R = $\sf{\dfrac{3}{5}}$ : $\sf{\dfrac{1}{5}}$ : $\sf{\dfrac{1}{5}}$

∴ New Profit Sharing Ratio of P, Q and R = 3 : 1 : 1