Answer
(a) The spheres are: $q_{B}= -2.0 \mu C$ and $q_{D}= +12 \mu C$
(b) The spheres are: $q_{A}= -8.0 \mu C$, $q_{C}= +5 \mu C$ and $q_{D}= +12 \mu C$
(c) The number of electrons to be added to one of these spheres to make it electrically neutral is $1.875\times10^{13}$
Work Step by Step
(a) As the charge on each sphere after they are separated is $+5 \mu C$, the resultant charge after they are brought to each other should be $(+5 \mu C\times2)=+10 \mu C$.
From the the given charges, if $q_{B}= -2.0 \mu C$, and $q_{D}= +12 \mu C$ brought to each other, the resultant charge will be $(-2.0 \mu C +12 \mu C)=+10 \mu C$.
After they are separated, the charge on each sphere will be $(+10 \mu C\div2)=+5 \mu C$.
(b) As the charge on each sphere after they are separated is $+3 \mu C$, the resultant charge after they are brought to each other should be $(+3 \mu C\times3)=+9 \mu C$.
From the the given charges, if $q_{A}= -8.0 \mu C$, $q_{C}=+5 \mu C$ and $q_{D}= +12 \mu C$ are brought to each other, the resultant charge will be $(-8.0 \mu C + 5 \mu C + 12 \mu C)= +9 \mu C$.
After they are separated, the charge on each sphere will be $(+9 \mu C\div3)=+3 \mu C$.
(c) To make one of the sphere having charge $+3 \mu C$ electrically neutral, one should add additional $-3 \mu C$ charge to it.
Charge of an electron $=-1.60\times10^{-19} C$
Therefore number of electrons to be added to make one of the sphere electrically neutral $=[-3 \mu C \div(1.6\times10^{-19})]=1.875\times10^{13}$
