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Keshav, Nirmal and Pankaj are partners sharing profits and losses in the ratio of 4 : 3 : 2. Nirmal retires and the goodwill is valued at Rs. 72,000. Keshav and Pankaj decided to share future profits and losses in the ratio of 5 : 3. Gaining Ratio of Keshav and Pankaj is:

Solution

✅ Correct Option: 1

Old Profit Sharing Ratio:

Keshav : Nirmal : Pankaj = 4 : 3 : 2

Keshav's old share = 49\frac{4}{9}

Pankaj's old share = 29\frac{2}{9}

New Profit Sharing Ratio (after Nirmal's retirement):

Keshav : Pankaj = 5 : 3

Keshav's new share = 58\frac{5}{8}

Pankaj's new share = 38\frac{3}{8}


Gaining Ratio = New Share - Old Share

For Keshav:

Gain = 58−49=45−3272=1372\frac{5}{8} - \frac{4}{9} = \frac{45-32}{72} = \frac{13}{72}

For Pankaj:

Gain = 38−29=27−1672=1172\frac{3}{8} - \frac{2}{9} = \frac{27-16}{72} = \frac{11}{72}

Gaining Ratio = 1372:1172\frac{13}{72} : \frac{11}{72} = 13 : 11

Expressing this as fractions of the total gain:

  • Keshav gains = 1324\frac{13}{24} (since 13 + 11 = 24)
  • Pankaj gains = 1124\frac{11}{24}

Gaining Ratio = 1324\frac{13}{24} : 1124\frac{11}{24}

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