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Sindhu, Neha and Priya are partners, sharing profits in the ratio of 5:3:2. Calculate the new profit sharing ratio and gaining ratio if Neha retires:

Solution

✅ Correct Option: 3

Old profit sharing ratio: Sindhu : Neha : Priya = 5:3:2

When Neha retires and nothing is mentioned about redistribution of her share, the remaining partners (Sindhu and Priya) continue in their old ratio.

New Profit Sharing Ratio:

Sindhu and Priya will share in their old ratio = 5:2

Therefore, New ratio = 5:2


Gaining Ratio:

Gaining Ratio = New Share - Old Share

Sindhu's old share = 510\frac{5}{10} = 12\frac{1}{2}

Sindhu's new share = 57\frac{5}{7} (as total of 5+2 = 7)

Sindhu's gain = 57−510\frac{5}{7} - \frac{5}{10} = 50−3570\frac{50-35}{70} = 1570\frac{15}{70} = 314\frac{3}{14}

Priya's old share = 210\frac{2}{10} = 15\frac{1}{5}

Priya's new share = 27\frac{2}{7}

Priya's gain = 27−210\frac{2}{7} - \frac{2}{10} = 20−1470\frac{20-14}{70} = 670\frac{6}{70} = 335\frac{3}{35}

Gaining Ratio = 314\frac{3}{14} : 335\frac{3}{35}

Multiplying by 70: 15:615:6 = 5:2

The gaining ratio is the same as the new profit sharing ratio because when nothing specific is mentioned, the remaining partners gain in their existing ratio.

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