Partnership

Retirement/Death

Medium

common

R, S and K are partners sharing profits in the ratio 4:3:2. R retires; S and K decided to share profits in future in the ratio of 5:3. Calculate the Gaining Ratio.

11:21

21:11

11:12

12:11

✅ Correct Option: 2

Given:

Old ratio (R:S:K) = 4:3:2
R retires
New ratio (S:K) = 5:3

Calculation of Gaining Ratio:

Gaining Ratio = New Share - Old Share

For S:

Old share = $\frac{3}{9}$ = $\frac{3}{9}$
New share = $\frac{5}{8}$

Gain of S = $\frac{5}{8} - \frac{3}{9}$ = $\frac{45 - 24}{72}$ = $\frac{21}{72}$

For K:

Old share = $\frac{2}{9}$
New share = $\frac{3}{8}$

Gain of K = $\frac{3}{8} - \frac{2}{9}$ = $\frac{27 - 16}{72}$ = $\frac{11}{72}$

Gaining Ratio = $\frac{21}{72} : \frac{11}{72}$ = 21:11

The gaining ratio represents the ratio in which S and K acquire R's share upon retirement. S gains a larger portion (21 parts) while K gains a smaller portion (11 parts) of R's original share.

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