X and Y are partners in a firm having capital balances Rs. 1,08,000 and Rs. 72,000, respectively. They admit Z into a partnership for $${\frac{1}{3}^{{\text{rd}}}}$$ share, and Z brings proportion ate amount of capital. The capital amount of Z is

Step 1: Find total capital of X and Y
X = 108,000
Y = 72,000

Total = 108,000 + 72,000 = 180,000

Step 2: Z is admitted for 1/3 share

This means:

Z’s capital should be 1/3 of total capital after admission

Let total capital after admission = T

Then:

Z’s share = (1/3)T
X and Y together = (2/3)T

But we already know:

X + Y = 180,000 = (2/3)T
Step 3: Find total capital (T)
2
3
𝑇
=
180
,
000
3
2
​

T=180,000
𝑇
=
180
,
000
×
3
2
=
270
,
000
T=180,000×
2
3
​

=270,000
Step 4: Find Z’s capital
𝑍
=
1
3
×
270
,
000
=
90
,
000
Z=
3
1
​

×270,000=90,000

Capital Ratio of share X & Y is 3:2
New Partner z Share 1/3

Now, X= 3/5-1/3=4/15
Y=2/5-1/3=1/15
Z=1/3*5*5=5/15

New Ratio=4:1:15
Now total Capital of X & Y is (108000+72000)=180000
Share Capital of Z is = 180000*5/10
=90000