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R, S and K are partners sharing profits in the ratio 8:6:4. On the retirement of R, the new profit sharing ratio between S and K was decided to be 5:3. The Gaining ratio is -

Solution

✅ Correct Option: 2

Old Ratio = R:S:K = 8:6:4

This means:

  • R's share = 818\frac{8}{18}
  • S's share = 618\frac{6}{18}
  • K's share = 418\frac{4}{18}

After R's retirement, New Ratio = S:K = 5:3

This means:

  • S's new share = 58\frac{5}{8}
  • K's new share = 38\frac{3}{8}

Gaining Ratio = New Share - Old Share

For S:

Gain = 58−618\frac{5}{8} - \frac{6}{18}

Converting to common denominator (LCM of 8 and 18 = 72):

Gain = 4572−2472=2172\frac{45}{72} - \frac{24}{72} = \frac{21}{72}

For K:

Gain = 38−418\frac{3}{8} - \frac{4}{18}

Gain = 2772−1672=1172\frac{27}{72} - \frac{16}{72} = \frac{11}{72}


Gaining Ratio = S's gain : K's gain = 2172:1172\frac{21}{72} : \frac{11}{72} = 21:11

The gaining ratio represents how R's share is distributed between the continuing partners S and K. When R retires with 818\frac{8}{18} share, S gains 2172\frac{21}{72} (which is 724\frac{7}{24}) and K gains 1172\frac{11}{72}, in the ratio 21:11.

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