Step 1: A quick example:
Say A and B share profits 3:2 and C gets 1/5 as a new partner. With no other information, A and B each give up a part of their share in proportion to 3:2.
Step 2: Work out the numbers:
A gives $\frac{3}{5} \times \frac{1}{5} = \frac{3}{25}$. B gives $\frac{2}{5} \times \frac{1}{5} = \frac{2}{25}$. So A and B sacrifice in the ratio 3:2, the same as their old ratio.
Step 3: General conclusion:
With no specific agreement, sacrificing ratio equals old profit sharing ratio. This is the default treatment used in admission problems.
Step 4: Other options:
Gaining ratio belongs to retirement. Capital ratio and equal ratio are not default rules.