The correct answer is $\frac{{M{U_X}}}{{M{U_Y}}} = \frac{{{P_X}}}{{{P_Y}}}$.
A discerning consumer is one who is able to compare the marginal utility of different goods and services and choose the combination that gives them the most satisfaction. The marginal utility of a good or service is the additional satisfaction that a consumer gets from consuming one more unit of that good or service. The marginal utility of a good or service will decrease as the consumer consumes more of that good or service.
A consumer will maximize their satisfaction when they are consuming the combination of goods and services that gives them the highest marginal utility per dollar spent. This is the point where the marginal utility of each good or service is equal to its price.
In mathematical terms, this can be expressed as follows:
$$\frac{{M{U_X}}}{{M{U_Y}}} = \frac{{{P_X}}}{{{P_Y}}}$$
where $M{U_X}$ is the marginal utility of good $X$, $M{U_Y}$ is the marginal utility of good $Y$, $P_X$ is the price of good $X$, and $P_Y$ is the price of good $Y$.
If the marginal utility of good $X$ is greater than the marginal utility of good $Y$, then the consumer can increase their satisfaction by consuming more of good $X$ and less of good $Y$. Conversely, if the marginal utility of good $X$ is less than the marginal utility of good $Y$, then the consumer can increase their satisfaction by consuming more of good $Y$ and less of good $X$.
Only when the marginal utility of each good or service is equal to its price will the consumer be maximizing their satisfaction.