Question

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.

Answer 1

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

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

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

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