Question

Ashok, Anil and Ajay are partners sharing profits and losses in the ratio of 1/2,3/10 and 1/5. Anil retires from the firm. Ashok and Ajay decide to share future profits in the ratio of 3:2. Calculate the Gaining ratio.​
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Answer 1

ANSWER :

• ❖ If Ashok, Anil and Ajay are partners sharing profits and losses in the ratio of $\sf{\dfrac{1}{2}}$ , $\sf{\dfrac{3}{10}}$ and $\sf{\dfrac{1}{5}}$ and on the retirement of Anil, Ashok and Ajay decide to share future profits in the ratio of 3 : 2; then the Gaining Ratio of Ashok and Ajay will be 1 : 2.

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SOLUTION :

❒ Given :-

• Ashok, Anil and Ajay are partners sharing profits and losses in the ratio of $\sf{\dfrac{1}{2}}$ , $\sf{\dfrac{3}{10}}$ and $\sf{\dfrac{1}{5}}$.

• After the retirement of Anil, Ashok and Ajay decide to share future profits in the ratio of 3 : 2.

❒ To Calculate :-

• Gaining Ratio of Ashok and ajay = ?

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❒ Calculation :-

It is given that,

• ✠ Ashok, Anil and Ajay are partners sharing profits and losses in the ratio of $\sf{\dfrac{1}{2}}$ , $\sf{\dfrac{3}{10}}$ and $\sf{\dfrac{1}{5}}$.

∴ Old Profit Sharing Ratio of Ashok, Anil and Ajay = $\sf{\dfrac{1}{2}}$ : $\sf{\dfrac{3}{10}}$ : $\sf{\dfrac{1}{5}}$

➜ Old Profit Sharing Ratio of Ashok, Anil and Ajay = $\sf{\dfrac{5}{10}}$ : $\sf{\dfrac{3}{10}}$ : $\sf{\dfrac{2}{10}}$

➜ Old Profit Sharing Ratio of Ashok, Anil and Ajay = 5 : 3 : 2.

Thus,

• Old Share of Profit of Ashok = $\sf{\dfrac{5}{10}}$

• Old Share of Profit of Anil = $\sf{\dfrac{3}{10}}$
• Old Share of Profit of Ajay = $\sf{\dfrac{2}{10}}$

Again,

• ✠ After the retirement of Anil, Ashok and Ajay decide to share future profits in the ratio of 3 : 2.

Thus,

• New Share of Profit of Ashok = $\sf{\dfrac{3}{5}}$

• New Share of Profit of Ajay = $\sf{\dfrac{2}{5}}$

We know that,

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

Using this formula, we get,

• ★ Gain of Ashok = New Share of Ashok - Old Share of Ashok

⇒ Gain of Ashok = $\sf{\dfrac{3}{5}}$ - $\sf{\dfrac{5}{10}}$

⇒ Gain of Ashok = $\sf{\dfrac{3 \times 2}{5 \times 2}}$ - $\sf{\dfrac{5}{10}}$

⇒ Gain of Ashok = $\sf{\dfrac{6}{10}}$ - $\sf{\dfrac{5}{10}}$

⇒ Gain of Ashok = $\sf{\dfrac{6 - 5}{10}}$

⇒ Gain of Ashok = $\sf{\dfrac{1}{10}}$

And,

• ★ Gain of Ajay = New Share of Ajay - Old Share of Ajay

⇒ Gain of Ajay = $\sf{\dfrac{2}{5}}$ - $\sf{\dfrac{2}{10}}$

⇒ Gain of Ajay = $\sf{\dfrac{2 \times 2}{5 \times 2}}$ - $\sf{\dfrac{2}{10}}$

⇒ Gain of Ajay = $\sf{\dfrac{4}{10}}$ - $\sf{\dfrac{2}{10}}$

⇒ Gain of Ajay = $\sf{\dfrac{4 - 2}{10}}$

⇒ Gain of Ajay = $\sf{\dfrac{2}{10}}$

Therefore,

• ✪ Gaining Ratio of Ashok and Ajay = Gain of Ashok : Gain of Ajay

➨ Gaining Ratio of Ashok and Ajay = $\sf{\dfrac{1}{10}}$ : $\sf{\dfrac{2}{10}}$

∴ Gaining Ratio of Ashok and Ajay = 1 : 2.