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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

Keshav's gain = 58−49\frac{5}{8} - \frac{4}{9}

Converting to common denominator (LCM of 8 and 9 = 72):

= 4572−3272=1372\frac{45}{72} - \frac{32}{72} = \frac{13}{72}

Pankaj's gain = 38−29\frac{3}{8} - \frac{2}{9}

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

Gaining Ratio = 1372:1172\frac{13}{72} : \frac{11}{72} = 13 : 11 = 13/24 : 11/24

The gaining ratio represents the share in which Keshav and Pankaj acquire Nirmal's share. Since their combined gain must equal Nirmal's share of 39\frac{3}{9}, we express it as parts of the total: Keshav gains 13 out of 24 parts and Pankaj gains 11 out of 24 parts.

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