Mayank and Nayank share profits in the ratio 2:1. Riya is admitted as a partner for a 1/6 share of profit. The remaining profit will be shared by the old partners in their old ratio. What is the new profit-sharing ratio?

Correct answer: Mayank : Nayank : Riya = 10 : 5 : 3

Riya receives 1/6 of the profit, leaving 1 − 1/6 = 5/6 for the old partners. Mayank receives 2/3 of this remainder, or (5/6) × (2/3) = 5/9. Nayank receives 1/3 of the remainder, or (5/6) × (1/3) = 5/18. Expressing all shares with denominator 18 gives 10/18 : 5/18 : 3/18, so the new ratio is 10:5:3.