A metallic sphere $\text{A}$ is given positive charge whereas the another identical metallic sphere $\text{B}$ of exactly same mass as of $\text{A}$ is given an equal amount of negative charge then,

The correct option is D Mass of $\text{B}$ increases
Sphere $\text{A}$ is given positive charge, which means that electrons have been extracted from sphere $\text{A}$.

$\Rightarrow$ Mass of sphere $\text{A}\downarrow$

Sphere $\text{B}$ has been given negative charge, i.e. excess electrons have been transferred to it.

$\Rightarrow$ Mass of sphere $\text{B}\uparrow$

$\begin{array}{c}\text{Why this question ?}\\ \text{Bottom line: Presence of negative charge means addition}\\ \text{of excess electrons, thus addition of}\\ \text{extra mass to the body.}\end{array}$