Question

Ram and Sham are partners in a firm sharing profit in the ratio of 3:2. They admitted Ghnashyam as a new partner Ram surrenders 1/4th of his share and Sham surrendered 1/3rd of his share in the favour of Ghanshyam. Calculate new profit sharing ratio of Ram, Sham and Ghnashyam:

Answer 1

ANSWER :

• ❖ If Ram and Shyam are partners in a firm sharing profits in the ratio of 3 : 2 and they admit Ghanshyam as a new partner when Ram surrenders 1/4th of his share and Shyam surrenders 1/3rd of his share in favour of Ghanshyam; then New Profit Sharing Ratio among Ram, Shyam and Ghanshyam is 27 : 16 : 17.

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SOLUTION :

❒ Given :-

• Ram and Shyam are partners in a firm sharing profits in the ratio of 3 : 2.

• Ghanshyam was admitted as a new partner.

• Ram surrendered 1/4th of his share and Shyam 1/3rd of his share in favour of Ghanshyam.

❒ To Calculate :-

• New Profit Sharing Ratio of Ram, Shyam and Ghanshyam = ?

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❒ Calculation :-

It is given that,

• Ram and Shyam are partners in a firm sharing profits in the ratio of 3 : 2.

So,

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

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

Again,

• Ram surrendered $\sf{\dfrac{1}{4}}$ th of his share in favour of Ghanshyam.

So,

• ✎ Ram's Sacrifice = $\sf{\dfrac{1}{4}}$ th of $\sf{\dfrac{3}{5}}$

⇒ Ram's Sacrifice = $\sf{\dfrac{1}{4}}$ × $\sf{\dfrac{3}{5}}$

⇒ Ram's Sacrifice = $\sf{\dfrac{3}{20}}$

And,

• Shyam surrendered $\sf{\dfrac{1}{3}}$ rd of his share in favour of Ghanshyam.

So,

• ✎ Shyam's Sacrifice = $\sf{\dfrac{1}{3}}$ rd of $\sf{\dfrac{2}{5}}$

⇒ Shyam's Sacrifice = $\sf{\dfrac{1}{3}}$ × $\sf{\dfrac{2}{5}}$

⇒ Shyam's Sacrifice = $\sf{\dfrac{2}{15}}$

Therefore,

• ★ New Share of Ram = Old Share of Ram - Ram's Sacrifice

➜ New Share of Ram = $\sf{\dfrac{3}{5} - \dfrac{3}{20}}$

➜ New Share of Ram = $\sf{\dfrac{12 - 3}{20}}$

➜ New Share of Ram = $\sf{\dfrac{9}{20}}$

➜ New Share of Ram = $\sf{\dfrac{9 \times 3}{20 \times 3}}$

➜ New Share of Ram = $\sf{\dfrac{27}{60}}$

And,

• ★ New Share of Shyam = Old Share of Shyam - Shyam's Sacrifice

➜ New Share of Shyam = $\sf{\dfrac{2}{5} - \dfrac{2}{15}}$

➜ New Share of Shyam = $\sf{\dfrac{6 - 2}{15}}$

➜ New Share of Shyam = $\sf{\dfrac{4}{15}}$

➜ New Share of Shyam = $\sf{\dfrac{4 \times 4}{15 \times 4}}$

➜ New Share of Shyam = $\sf{\dfrac{16}{60}}$

However,

• ★ Share of Ghanshyam = Ram's Sacrifice + Shyam's Sacrifice

➜ Share of Ghanshyam = $\sf{\dfrac{3}{20} + \dfrac{2}{15}}$

➜ Share of Ghanshyam = $\sf{\dfrac{9 + 8}{60}}$

➜ Share of Ghanshyam = $\sf{\dfrac{17}{60}}$

Thus,

• ✪ New Profit Sharing Ratio among Ram, Shyam and Ghanshyam = New Share of Ram : New Share of Shyam : Share of Ghanshyam

➨ New Profit Sharing Ratio among Ram, Shyam and Ghanshyam = $\sf{\dfrac{27}{60}}$ : $\sf{\dfrac{17}{60}}$ : $\sf{\dfrac{17}{60}}$

∴ New Profit Sharing Ratio among Ram, Shyam and Ghanshyam = 27 : 16 : 17