A and B share profits in the ratio of 7 : 3. They admitted C as a partner. A surrenders $${\frac{1}{4}^{{\text{th}}}}$$ of his share and B $${\frac{1}{3}^{{\text{rd}}}}$$ share to C. New profit sharing ratio among A, B and C would be:

The correct answer is $\boxed{\text{C}}$.

Initially, A and B share profits in the ratio of 7 : 3. This means that A’s share is $\frac{7}{10}$ of the total profit and B’s share is $\frac{3}{10}$ of the total profit.

When C is admitted as a partner, A surrenders $\frac{1}{4}$ of his share and B surrenders $\frac{1}{3}$ of his share to C. This means that A’s new share is $\frac{7}{10} – \frac{1}{4} = \frac{21}{40}$ of the total profit and B’s new share is $\frac{3}{10} – \frac{1}{3} = \frac{3}{20}$ of the total profit.

The new profit sharing ratio among A, B and C is $\frac{21}{40} : \frac{3}{20} : \frac{17}{40} = 12 : 6 : 7$.