CUET UG 2025 — Accountancy Partnership

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

This means:

• R's share = $\frac{8}{18}$188​
• S's share = $\frac{6}{18}$186​
• K's share = $\frac{4}{18}$184​

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

This means:

• S's new share = $\frac{5}{8}$85​
• K's new share = $\frac{3}{8}$83​

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Gaining Ratio = New Share - Old Share

For S:
Gain = $\frac{5}{8} - \frac{6}{18}$85​−186​

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

Gain = $\frac{45}{72} - \frac{24}{72} = \frac{21}{72}$7245​−7224​=7221​

For K:
Gain = $\frac{3}{8} - \frac{4}{18}$83​−184​

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

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Gaining Ratio = S's gain : K's gain = $\frac{21}{72} : \frac{11}{72}$7221​:7211​ = 21:11

The gaining ratio represents how R's share is distributed between the continuing partners S and K. When R retires with $\frac{8}{18}$188​ share, S gains $\frac{21}{72}$7221​ (which is $\frac{7}{24}$247​) and K gains $\frac{11}{72}$7211​, in the ratio 21:11.