X and Y are partners sharing profits in the ratio 5:3. They admitted Z for 1/5th profits, for which he paid ₹60,000 against capital and ₹30,000 against goodwill. Find the capital balance for each partner taking Z's capital as base capital.

₹1,50,000; ₹90,000 and ₹60,000

The correct answer is option 3- ₹1,50,000; ₹90,000 and ₹60,000.

Let total share = 1
Z share = 1/5
Remaining share after Z = 1 - 1/5
                                      = 4/5
This 4/5th share is divided between old partners in their old share
Old ratio between X & Y = 5:3

X's new share = 5/8 x 4/5
                        = 20/40
Y's new share = 3/8 x 4/5
                       = 12/40

New ratio = 20/40 : 12/40 : 1/5
                = 20/40 : 12/40 : 8/40
                = 20:12:8 or 5 :3 :2.

Capital brought by Z = 60,000
Total capital of the firm on the basis of Z share = 60,000 x 5
                                                                          = 3,00,000

X's capital = 3,00,000 x 5/10
                = 1,50,000
Y's capital = 3,00,000 x 3/10
                = 90,000

So, capital of partners are X=1,50,000 Y= 90,000 & Z= 60,000.