A and B share profits in (9:6). C is admitted for (1/3) share and the remaining profit is shared in the old ratio. What is the new ratio?

Correct answer: (6:4:5)

Direct answer: Option A, 6:4:5, is correct. The old ratio of A and B is 9:6, which simplifies to 3:2. C receives 1/3, so only 2/3 remains for A and B. That remaining 2/3 must be divided in the old ratio 3:2. A receives (2/3)×(3/5)=2/5, and B receives (2/3)×(2/5)=4/15. C receives 1/3 = 5/15. Expressing every share with denominator 15 gives A 6/15, B 4/15 and C 5/15, hence 6:4:5. Option A is therefore correct. Option B, 9:6:3, treats the original figures as if they could simply be joined with C’s share; their total does not represent the required normalized distribution. Option C gives C three parts instead of five in the common denominator. Option D does not preserve the correct remaining-profit calculation. Exam cue: when the new partner gets a stated share and the remainder follows the old ratio, multiply the remainder by each old partner’s fraction.