Question

Vani Rani and Soni are partners in a firm sharing profits and losses in the ratio of 4:3:2.Soni retires from the firm.Vani and Rani agreed to share equally in future.​

Answer 1

Correct Question :-

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Vani, Rani and Soni are partners in a firm sharing profits and losses in the ratio of 4: 3: 2. Soni retires from the firm. Vani and Rani agreed to share equally in future. Calculate Gain Ratio of Vani and Rani.

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Answer :-

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In the attachment!!

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HOPE THIS HELPS YOU!!!!!

Answer 2

Given,

Vani Rani and Soni are partners in firm sharing profits and losses in the ratio of 4:3:2

To find,

Gain ratio when Vani and Rani agree to become equal partners.

Solution,

The gain ratio is the difference between the new ratio and the old ratio.

Mathematically,

Gain ratio = New ratio - Old ratio

Let $x$ be some variable where $4x, 3x, 2x$ is the share of Vani, Rani and Soni respectively.

Total share = $4x + 3x + 2x = 9x$

Calculating the old ratio for Vani = $\frac{4x}{ (4 + 3 + 2)x} = \frac{4}{9}$

Similarly, the old ratio of Rani = $\frac{3x}{ (4 + 3 + 2)x} = \frac{3}{9}$

The new ratio for both Rani and Vani is $= \frac{1}{2}$

Now, calculating the gain Ratio for Rani,

                                $= \frac{1}{2} - \frac{3}{9} \\= \frac{9 - 2*3}{18}\\= \frac{9 - 6}{18} \\= \frac{3}{18} = \frac{1}{6}$

Now, calculating the gain Ratio for Vani,

                                 $= \frac{1}{2} - \frac{4}{9} \\= \frac{9 - 2*4}{18}\\= \frac{9 - 8}{18} \\= \frac{2}{18} = \frac{1}{9}$

Therefore, the gain ratio for Vani is $\frac{1}{9}$, and that for Rani is $\frac{1}{6}.$