Question

6. B and N are partners in a firm sharing profits in the ratio of 3:2. They admit
S as a partner for 1/4th share in the profits. S acquires his share from B and N
in the ratio of 2 : 1. The new profit-sharing ratio will be :​

Answer 1

ANSWER :

• ❖ If B and N are partners in a firm sharing profits and losses in the ratio of 3 : 2 and S is admitted as partner with 1/4 th share in profit which he acquires from B and N in the ratio of 2 : 1; then the New Profit Sharing Ratio of B, N and S will be 26 : 19 : 15.

___________________________________________________________

SOLUTION :

❒ Given :-

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

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

• S acquires his share from B and N in the ratio of 2 : 1.

❒ To Calculate :-

• New Profit Sharing Ratio among B, N and S = ?

___________________________________________

❒ Calculation :-

It is given that,

• S is admitted as partner with $\rm{\dfrac{1}{4}}$ th share in profit.

• S acquires his share from B and N in the ratio of 2 : 1.

So,

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

⇒ S acquires share of profit from B =  $\sf{\dfrac{2}{3} \times \dfrac{1}{4}}$

⇒ S acquires share of profit from B =  $\sf{\dfrac{2}{12}}$

And,

• S acquires share of profit from N = $\sf{\dfrac{1}{3}}$ th of $\sf{\dfrac{1}{4}}$

⇒ S acquires share of profit from N =  $\sf{\dfrac{1}{3} \times \dfrac{1}{4}}$

⇒ S acquires share of profit from N =  $\sf{\dfrac{1}{12}}$

Thus,

• ❍ Share of S = S acquires share of profit from B + S acquires share of profit from N

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

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

⇒ Share of S  = $\sf{\dfrac{3}{12}}$

Again,

• Old Profit Sharing Ratio of B and N is 3 : 2.

So,

• B's Old Share = $\sf{\dfrac{3}{5}}$

• N's Old Share = $\sf{\dfrac{2}{5}}$

Also,

• Share surrendered by B = $\sf{\dfrac{3}{12}}$

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

We know that,

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

Using this formula, we get,

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

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

➨ B's New Share = $\tt{\dfrac{36 - 10}{60}}$

➨ B's New Share = $\tt{\dfrac{26}{60}}$

Similarly,

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

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

➨ N's New Share = $\tt{\dfrac{24 - 5}{60}}$

➨ N's New Share = $\tt{\dfrac{19}{60}}$

And,

• ★ Share of S =  $\tt{\dfrac{3}{12}}$

➨ Share of S = $\tt{\dfrac{3 \times 5}{12 \times 5}}$

➨ Share of S = $\tt{\dfrac{15}{60}}$

Hence,

• ✪ New Profit Sharing Ratio of B, N and S = New Share of B : New Share of N : Share of S

⇒ New Profit Sharing Ratio of B, N and S = $\tt{\dfrac{26}{60}}$ : $\tt{\dfrac{19}{60}}$ : $\tt{\dfrac{15}{60}}$

∴ New Profit Sharing Ratio of B, N and S = 26 : 19 : 15

Answer 2

Answer:

b =2/3×1/4=2/12

n=1/3×1/4=1/12

s=2+1/12=3/12

old share-new share

b=3/5

n=2/5

new share

b=3/2

n=1/12

b=3/5-3/12 = 36-10/60

=26/60

n=2/5-1/12 = 24-5/60

=19/60

s=3/12×5/5= 15/60

26:19:15