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A and B are partners in a firm sharing profits in the ratio of 3:2. They admit C as a partner for 1/3 share, the sacrificing ratio between A and B is

Solution

✅ Correct Option: 1

Given Information:

  • Old ratio of A and B = 3:2
  • C is admitted for 1/3 share

Finding Old Shares:

A's old share = 35\frac{3}{5}

B's old share = 25\frac{2}{5}


Finding New Shares:

C's share = 13\frac{1}{3}

Remaining share for A and B = 1−13=231 - \frac{1}{3} = \frac{2}{3}

This remaining share will be divided between A and B in their old ratio of 3:2.

A's new share = 23×35=615=25\frac{2}{3} \times \frac{3}{5} = \frac{6}{15} = \frac{2}{5}

B's new share = 23×25=415\frac{2}{3} \times \frac{2}{5} = \frac{4}{15}


Calculating Sacrifice:

Sacrifice = Old Share - New Share

A's sacrifice = 35−25=15\frac{3}{5} - \frac{2}{5} = \frac{1}{5}

B's sacrifice = 25−415=615−415=215\frac{2}{5} - \frac{4}{15} = \frac{6}{15} - \frac{4}{15} = \frac{2}{15}


Sacrificing Ratio:

Sacrificing Ratio = A's sacrifice : B's sacrifice

= 15:215\frac{1}{5} : \frac{2}{15}

= 315:215\frac{3}{15} : \frac{2}{15}

= 3:2

The sacrificing ratio remains the same as the old profit sharing ratio because both partners sacrificed in the same proportion as they were sharing profits earlier.

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