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A, B, and C were in partnership, sharing profits in the ratio of 3:2:1 respectively, B retires and the new profit sharing ratio between A and C is 3:2 . The gaining ratio is .

Solution

✅ Correct Option: 1

Old Profit Sharing Ratio: A:B:C = 3:2:1

Converting to fractions:

  • A's old share = 36\frac{3}{6} = 12\frac{1}{2}
  • B's old share = 26\frac{2}{6} = 13\frac{1}{3}
  • C's old share = 16\frac{1}{6}

New Profit Sharing Ratio (after B retires): A:C = 3:2

Converting to fractions:

  • A's new share = 35\frac{3}{5}
  • C's new share = 25\frac{2}{5}

Calculating Gain for each partner:

Gain = New share - Old share

A's gain = 35\frac{3}{5} - 12\frac{1}{2} = 610\frac{6}{10} - 510\frac{5}{10} = 110\frac{1}{10}

C's gain = 25\frac{2}{5} - 16\frac{1}{6} = 1230\frac{12}{30} - 530\frac{5}{30} = 730\frac{7}{30}


Gaining Ratio:

A:C = 110\frac{1}{10} : 730\frac{7}{30}

Multiplying both sides by 30 to remove fractions:

A:C = 3 : 7

Correct Option: 1

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