C is admitted for 41 share of profits.
Remaining share for old partners A and B = 1−41=43
This remaining 43 share will be divided between A and B in their old ratio of 2:1.
A's new share = 43×32=42=21
B's new share = 43×31=41
C's share = 41
New Profit Sharing Ratio = 21:41:41
Converting to simple ratio by multiplying by 4:
A : B : C = 2 : 1 : 1
The capitals of partners (Rs. 45,000, Rs. 15,000, and Rs. 20,000) mentioned in the question are their adjusted capitals which will now need to be brought in proportion to this new profit sharing ratio of 2:1:1 through further capital adjustments.