Question

[As. Gaining Ratio - 4:3 and New Ratio - 1.1.] Q. 9 (A). On Ist April, 2018 Ashish, Namish and Aman were partners sharing profits and losses in the ratio of 2/5, 2/5 and 1/5 respectively. On this date Namish retires. The new profit sharing ratio of Ashish and Aman will be 3/4 and 1/4 respectively. Calculate gaining ratio.​

Answer 1

Answer: Gaining ratio of Ashish and Aman is 7 : 1.

Step-by-step explanation:

Given that,

Ashish, Namish and Aman share profits and losses in ratio 2/5 : 2/5 : 1/5

Namish retires. Ashish And Aman's new profit sharing ratio = 3/4 : 1/4 or 3 : 1

Old ratio of the three partners = 2/5 : 2/5 : 1/5 or 2 : 2 : 1

We know that,

Gain ratio = New ratio - Old ratio

So,

Ashish's gain ratio = 3/4 - 2/5

= (15 - 8)/20

= 7/20

Aman's gain ratio = 1/4 - 1/5

= (5 - 4)/20

= 1/20

Thus, Gain ratio of Ashok and Ajay is 7/20 : 1/20 or 7 : 1.

Gain Ratio:

The ratio in which the existing partners acquire the share of retiring partner is called Gain ratio.

Answer 2

ANSWER :

• ❖ If on 1st April, 2018, Ashish, Namish and Aman were partners sharing profits and losses in the ratio of 2/5, 2/5 and 1/5 respectively and on this date Namish retires and the new profit sharing ratio of Ashish and Aman became 3/4 and 1/4 respectively; then the Gaining Ratio of Ashish and Aman will be 7/20 and 1/20 or 7 : 1.

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SOLUTION :

❒ Given :-

• Ashish, Namish and Aman were partners sharing profits and losses in the ratio of $\rm{\dfrac{2}{5}}$, $\rm{\dfrac{2}{5}}$ and $\rm{\dfrac{1}{5}}$ respectively.

• After Namish retired, new profit sharing ratio of Ashish and Aman was $\rm{\dfrac{3}{4}}$ and $\rm{\dfrac{1}{4}}$ respectively.

❒ To Calculate :-

• Gaining Ratio of Ashish and Aman = ?

❒ Required Formula :-

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

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❒ Calculation :-

It is given that,

• After Namish retired, new profit sharing ratio of Ashish and Aman was $\rm{\dfrac{3}{4}}$ and $\rm{\dfrac{1}{4}}$ respectively.

It means,

• New Share of Ashish = $\sf{\dfrac{3}{4}}$

• New Share of Aman = $\rm{\dfrac{1}{4}}$

Again,

• Ashish, Namish and Aman were partners sharing profits and losses in the ratio of $\rm{\dfrac{2}{5}}$, $\rm{\dfrac{2}{5}}$ and $\rm{\dfrac{1}{5}}$ respectively.

It means,

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

• Old Share of Aman = $\rm{\dfrac{1}{5}}$

Now,

Using the formula of Gain, we get,

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

⇒ Gain of Ashish = $\sf{\dfrac{3}{4}}$ - $\sf{\dfrac{2}{5}}$

⇒ Gain of Ashish = $\sf{\dfrac{15 - 8}{20}}$

⇒ Gain of Ashish = $\sf{\dfrac{7}{20}}$

And,

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

⇒ Gain of Aman = $\sf{\dfrac{1}{4}}$ - $\sf{\dfrac{1}{5}}$

⇒ Gain of Aman = $\sf{\dfrac{5 - 4}{20}}$

⇒ Gain of Aman = $\sf{\dfrac{1}{20}}$

Therefore,

• ✪ Gaining Ratio of Ashish and Aman = Gain of Ashish : Gain of Aman

➨ Gaining Ratio of Ashish and Aman = $\sf{\dfrac{7}{20}}$ : $\sf{\dfrac{1}{20}}$

∴ Gaining Ratio of Ashish and Aman = 7 : 1