A, B and Care partners sharing profits in the ratio of 3 : 3 : 4. They decide to share the future profits equally. The sacrifice or gain of partners are:

The correct option is: A gains 1/30; B gains 1/30; C sacrifices 2/30.

To determine the sacrifice or gain of each partner, we compare their old profit-sharing ratios with their new profit-sharing ratios.

The formula to calculate the sacrificing or gaining share for a partner is:
$$Sacrificing\; Share=Old\; Share-New\; Share$$
If the result is positive, the partner has sacrificed a portion of their share. If the result is negative, the partner has gained a portion of the share.

Let us write down the given ratios:
Old profit-sharing ratio of A, B, and C = 3 : 3 : 4
Therefore, the old shares are:
$Old\; Share\; of\; A=\frac{3}{3+3+4}=\frac{3}{10}$
$Old\; Share\; of\; B=\frac{3}{10}$
$Old\; Share\; of\; C=\frac{4}{10}$

The partners decide to share future profits equally.
New profit-sharing ratio of A, B, and C = 1 : 1 : 1
Therefore, the new shares are:
$New\; Share\; of\; A=\frac{1}{3}$
$New\; Share\; of\; B=\frac{1}{3}$
$New\; Share\; of\; C=\frac{1}{3}$

Now, let us calculate the sacrifice or gain for each partner:

For Partner A:
$$Share\; change\; of\; A=\frac{3}{10}-\frac{1}{3}$$
Taking the common denominator as 30:
$$Share\; change\; of\; A=\frac{9-10}{30}=-\frac{1}{30}$$
Since the result is negative, A gains 1/30.

For Partner B:
$$Share\; change\; of\; B=\frac{3}{10}-\frac{1}{3}$$
Taking the common denominator as 30:
$$Share\; change\; of\; B=\frac{9-10}{30}=-\frac{1}{30}$$
Since the result is negative, B gains 1/30.

For Partner C:
$$Share\; change\; of\; C=\frac{4}{10}-\frac{1}{3}$$
Taking the common denominator as 30:
$$Share\; change\; of\; C=\frac{12-10}{30}=\frac{2}{30}$$
Since the result is positive, C sacrifices 2/30.

Thus, A gains 1/30, B gains 1/30, and C sacrifices 2/30.