X and Y are in partnershop sharig profits and lesses in the ratio of 3 : 2. They capitals of X and Y after adjustment are RS.80,000 and RS.60,000 respectively. They admit Z as a third partner who is to contribute proportinate capital to acquire a 1/5th share of total capital of the new firm equally from both the partners X and Y. Calculate capital to be brought in by Z. Also calculate new profit-sharing ratio of the partners in the new firm.

Explanation

Let the total share =1, Z's share = 1/5th, Remaining share of X and Y =1-1/5=4/5.
1. Calculation of Z's Capital on the Basis of X's Capital and Y's Capital:
Step 1. Adjusted combined capital of X and Y = RS.80,000+RS.60,000=RS.1,40,000.
Step 2. Calculation of Total Capital of the Reconstituted Firm:
Total capital of the new firm
=Total adjusted capital of X and Y `xx` Reciprocal of total share of X and Y `=RS.1,40,000xx5//4=RS.1,75,000`.
Step 3. Calculation of Proportionatc Capital of Incoming Partner (Z):
Proportionate capital of `Z =RS.1,75,000xx1//5=RS.35,000`
2. `{:(,"Calculation of New Profit-sharing Ratio:",X,Y,Z),((a),"Their Existing Shares",3//5,2//5,....),((b),"Share transferred to Z",1//10,1//10,(1//10+1//10)),((c),"Their New Share (a-b)",5//10,3//10,2//10),((d),"New Profit-sharing Ratio of X,Y and Z=5//10:3//10:2//10=5:3:2.,,):}`.