C is admitted with 1/4th share in profits. This means the remaining share for old partners A and B = 1 - 1/4 = 3/4
Since A and B were sharing profits in ratio 2:1, they will now share this remaining 3/4 in the same ratio.
A's new share = 3/4 × 2/(2+1) = 3/4 × 2/3 = 1/2
B's new share = 3/4 × 1/(2+1) = 3/4 × 1/3 = 1/4
C's share = 1/4
New profit sharing ratio = A:B:C = 1/2 : 1/4 : 1/4 = 2:1:1
C brings Rs. 30,000 as capital for 1/4 share in profits.
When capitals are to be adjusted in profit sharing ratio, C's capital should be proportionate to his profit share.
If C's capital of Rs. 30,000 represents 1/4 share, then:
Total capital of the firm = Rs. 30,000 × 4 = Rs. 1,20,000
Now, capitals should be in the new profit sharing ratio 2:1:1
A's capital = Total capital × A's share ratio = Rs. 1,20,000 × 2/4 = Rs. 60,000
B's capital = Rs. 1,20,000 × 1/4 = Rs. 30,000
C's capital = Rs. 30,000
Therefore, the capital of A will be Rs. 60,000.