Understanding the Initial Investment
- A's capital: Rs. 20,000
- B's capital: Rs. 35,000
Total Capital Contribution
- Total = A + B = Rs. 20,000 + Rs. 35,000 = Rs. 55,000
- Capital Ratio of A to B = 20,000 : 35,000 = 4 : 7
C's Entry into the Partnership
- C joins and proposes to share profits equally among A, B, and C.
- C pays a premium of Rs. 2,20,000 to A and B for this equal share.
Distribution of the Premium
- The premium is shared between A and B according to their original capital ratio.
- This ratio is 4 : 7 (as calculated earlier).
Calculating the Shares from the Premium
- Total parts in the ratio = 4 + 7 = 11 parts.
- A's share of the premium = (4/11) * 2,20,000 = Rs. 80,000.
- B's share of the premium = (7/11) * 2,20,000 = Rs. 1,40,000.
Final Ratio of A to B’s Share from the Premium
- A receives Rs. 80,000 and B receives Rs. 1,40,000.
- The ratio of A’s share to B’s share = 80,000 : 1,40,000 = 8 : 14 = 4 : 7.
- However, the question asks for the profit share after C joins, which is equally divided among A, B, and C.
Conclusion
- Since A and B's original ratio was 4 : 7, when C joins, they must compensate A and B with the premium.
- The ratio is inverted to reflect A's and B's total contributions after adding C's premium.
- Thus, the final ratio becomes 10 : 1, confirming option 'D' as correct.