Question

A and B were partners in a firm sharing profits in the ratio of 5: 3. They admitted C and D as new partners. A surrendered 1/2 of his share in favour of C and B surrendered 1/2 of his share in favour of D. Calculate the new profit-sharing ratio of A, B, C and D. ​

Answer 1

ANSWER :

• ❖ If A and B were partners in a firm sharing profits in the ratio of 5 : 3; C and D were admitted as new partners and A surrendered 1/2th of his share in favour of C and B surrendered 1/2th of his share in favour of D; then the New Profit Sharing Ratio of A, B, C and D will be 5 : 3 : 5 : 3.

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SOLUTION :

❒ Given :-

• A and B were partners in a firm sharing profits in the ratio of 5 : 3.

• C and D were admitted as new partners.

• A surrendered $\sf{\dfrac{1}{2}}$ th of his share in favour of C.

• B surrendered $\sf{\dfrac{1}{2}}$ th of his share in favour of D.

❒ To Calculate :-

• New profit sharing ratio of A, B, C and D = ?

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❒ Calculation :-

Here,

• Old Profit Sharing Ratio of A and B = 5 : 3.

So,

• Old Share of A = $\sf{\dfrac{5}{8}}$

• Old Share of B = $\sf{\dfrac{3}{8}}$

Again,

• While admission of C as a partner, A surrendered $\sf{\dfrac{1}{2}}$ th of his share in favour of C.

So,

• ✠ Share Surrendered by A = $\sf{\dfrac{1}{2}}$ th of $\sf{\dfrac{5}{8}}$

➜ Share Sacrificed by A = $\sf{\dfrac{1}{2} \times \dfrac{5}{8}}$

➜ Share Sacrificed by A = $\sf{\dfrac{5}{16}}$

And,

• While admission of D as a partner, B surrendered $\sf{\dfrac{1}{2}}$ th of his share in favor of D.

So,

• ✠ Share Sacrificed by B = $\sf{\dfrac{1}{2}}$ th of $\sf{\dfrac{3}{8}}$

➜ Share Sacrificed by B = $\sf{\dfrac{1}{2} \times \dfrac{3}{8}}$

➜ Share Sacrificed by B = $\sf{\dfrac{3}{16}}$

Now,

• ★ New Share of A = Old Share of A - Share surrendered by A in favor of C

⇒ New Share of A = $\sf{\dfrac{5}{8} - \dfrac{5}{16}}$

⇒ New Share of A = $\sf{\dfrac{10 - 5}{16}}$

⇒ New Share of A = $\sf{\dfrac{5}{16}}$

And,

• ★ New Share of B = Old Share of B - Share Surrendered by B in favor of D

⇒ New Share of B = $\sf{\dfrac{3}{8} - \dfrac{3}{16}}$

⇒ New Share of B = $\sf{\dfrac{6 - 3}{16}}$

⇒ New Share of B = $\sf{\dfrac{3}{16}}$

However,

• ★ Share of C = Share Surrendered by A

⇒ Share of C = $\sf{\dfrac{5}{16}}$

And,

• ★ Share of D = Share Surrendered by B

⇒ Share of D = $\sf{\dfrac{3}{16}}$

Hence,

• ✪ New Profit Sharing Ratio of A, B, C and D = New Share of A : New Share of B : Share of C : Share of D

➨ New Profit Sharing Ratio of A, B, C and D = $\sf{\dfrac{5}{16}}$ : $\sf{\dfrac{3}{16}}$ : $\sf{\dfrac{5}{16}}$ : $\sf{\dfrac{3}{16}}$

∴ New Profit Sharing Ratio = 5 : 3 : 5 : 3