An atom has 25 protons , 30 neutrons and 25 electrons . What is the charge of the atom's nucleus?

The charge of the
nucleus of an atom with 25 protons is +25 regardless of the number of other particles. Protons
are the only charged particle in the nucleus. However, the overall charge of the atom is zero.
That's because protons in the nucleus and electrons outside the nucleus have opposite charges
and the sum of +25 and -25 is zero. The nuclear charge of any atom is given by its atomic
number. 

Here are the charges, locations and approximate masses of the
sub-atomic particles:

proton - in nucleus, charge = +1, mass = approximately
1 amu

neutron - in nucleus, charge = 0 (neutral), mass = approximately 1
amu

electron - outside nucleus, charge = -1, mass = approximately 0
amu 

(The mass of the electron is often neglected when calculating the mass
of an atom. It has a value of 5.49 x 10^(-4) amu, or 1/1840 of an amu.)