A and B share profits in the ratio 5:1. C is admitted for a 1/3 share of the profits. The remaining profits will be shared by A and B in the ratio 2:1. What will be the new profit-sharing ratio?

Correct answer: A : B : C = 4 : 2 : 3

C receives 1/3 of the profits, so the remaining share for A and B is 2/3. Dividing this remainder in the ratio 2:1 gives A's share as (2/3) × (2/3) = 4/9 and B's share as (2/3) × (1/3) = 2/9. C's share is 1/3 = 3/9. Therefore, the new ratio is 4:2:3. The original 5:1 ratio is not used directly because the question specifies that the remaining profit will be shared in the ratio 2:1. Exam tip: subtract the admitted partner's share from 1 first, then distribute the balance according to the stated ratio of the old partners.