In an examination, it is required to get $310$ marks of the aggregate marks to pass. A student gets $28\%$ marks and is declared failed by $93$ marks. What are the maximum aggregate marks a student can get?

Let the maximum aggregate marks be $M$.
The passing marks required are $310$.

The student scored $28\%$ of $M$ and failed by $93$ marks. This means if the student had scored $93$ more marks, they would have passed.

$$28\%\text{ of }M+93=310$$

$$\frac{28}{100}\times M=310-93$$

$$0.28\times M=217$$

$$M=\frac{217}{0.28}=\frac{21700}{28}$$

Dividing numerator and denominator by $7$:

$$M=\frac{3100}{4}=775$$

Hence, the maximum aggregate marks are $775$.