Suresh and Ramesh were partners in a firm sharing profits in 5:3 ratio. On 1-4-2013 they admitted Deepak as a new partner for 1/4th share. On 31st July, 2013 Karan was admitted as a new partner for 1/6th share which he acquired equally from Suresh, Ramesh and Deepak. Calculate the new profit sharing ratio of Suresh, Ramesh, Deepak and Karan.

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Solution

Share given to Deepak $\frac{1}{4}$ ; Remaining Share $= 1 - \frac{1}{4} = \frac{3}{4}$

Suresh's new share $= \frac{5}{8} o f \frac{3}{4} = \frac{15}{32}$

Ramesh's new share $= \frac{3}{8}$ of $\frac{3}{4} = \frac{9}{32}$

Deepak's share $= \frac{1}{4}$

New Ratio of Suresh, Ramesh and Deepak

$= \frac{15}{32} : \frac{9}{32} : \frac{1}{4} = \frac{15 : 9 : 8}{32} = 15 : 9 : 8$

Share given to Karan $= \frac{1}{6}$

He will acquire $\frac{1}{3}$ of $\frac{1}{6} = \frac{1}{18}$ each from Suresh, Ramesh and Deepak.

Hence, Suresh's new share $= \frac{15}{32} - \frac{1}{18} = \frac{135 - 16}{288} = \frac{119}{288}$

Ramesh's new share $= \frac{9}{32} - \frac{1}{18} = \frac{81 - 16}{288} = \frac{65}{288}$

Deepak's new share $= \frac{8}{32} - \frac{1}{18} = \frac{72 - 16}{288} = \frac{56}{288}$

Karan's share $= \frac{1}{6}$

New Ratio of Suresh, Ramesh, Deepak and Karan

$= \frac{119}{288} : \frac{65}{288} : \frac{56}{288} : \frac{1}{6} = \frac{119 : 65 : 56 : 48}{288} = 119 : 65 : 56 : 48$

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