Question

) A and B share profits in the ratio of 3 : 2 . They agreed to admit C on the condition that A will sacrifice 3/25th of his share of profits in favour of C and B will sacrifice 1/25th of his profits in favour of C. the new profit sharing ratio will be :
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Answer 1

New Profit sharing Ratio is 66 : 48 : 11

Explanation:

A surrenders $\frac{3}{25}^{th}$ to C of his share $\frac{3}{5}$ =  $\frac{3}{25}$ × $\frac{3}{5}$

                                                            = $\frac{9}{125}$

B surrenders $\frac{1}{25}^{th}$to C of his share $\frac{2}{5}$ = $\frac{1}{25}$ × $\frac{2}{5}$

                                                           = $\frac{2}{125}$

C's Share =  $\frac{9}{125}$ + $\frac{2}{125}$

                = $\frac{11}{125}$

A's New Share = $\frac{3}{5}$ - $\frac{9}{125}$

                         = $\frac{66}{125}$

B's New Share = $\frac{2}{5}$  - $\frac{2}{125}$

                         = $\frac{48}{125}$  

∴ New Profit Sharing Ratio of A : B : C is 66 : 48 : 11

Answer 2

Explanation:

A surrenders \frac{3}{25}^{th}253th to C of his share \frac{3}{5}53 =  \frac{3}{25}253 × \frac{3}{5}53

                                                            = \frac{9}{125}1259

B surrenders \frac{1}{25}^{th}251th to C of his share \frac{2}{5}52 = \frac{1}{25}251 × \frac{2}{5}52

                                                           = \frac{2}{125}1252

C's Share =  \frac{9}{125}1259 + \frac{2}{125}1252

                = \frac{11}{125}12511

A's New Share = \frac{3}{5}53 - \frac{9}{125}1259

                         = \frac{66}{125}12566

B's New Share = \frac{2}{5}52  - \frac{2}{125}1252

                         = \frac{48}{125}12548  

∴ New Profit Sharing Ratio of A : B : C is 66 : 48 : 11