CUET UG 2025 — Accountancy Partnership

Old Profit Sharing Ratio:
Keshav : Nirmal : Pankaj = 4 : 3 : 2

Keshav's old share = $\frac{4}{9}$94​
Pankaj's old share = $\frac{2}{9}$92​

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New Profit Sharing Ratio (after Nirmal's retirement):
Keshav : Pankaj = 5 : 3

Keshav's new share = $\frac{5}{8}$85​
Pankaj's new share = $\frac{3}{8}$83​

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Gaining Ratio = New Share - Old Share

Keshav's gain = $\frac{5}{8} - \frac{4}{9}$85​−94​

Converting to common denominator (LCM of 8 and 9 = 72):
= $\frac{45}{72} - \frac{32}{72} = \frac{13}{72}$7245​−7232​=7213​

Pankaj's gain = $\frac{3}{8} - \frac{2}{9}$83​−92​

= $\frac{27}{72} - \frac{16}{72} = \frac{11}{72}$7227​−7216​=7211​

Gaining Ratio = $\frac{13}{72} : \frac{11}{72}$7213​:7211​ = 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 $\frac{3}{9}$93​, we express it as parts of the total: Keshav gains 13 out of 24 parts and Pankaj gains 11 out of 24 parts.