Why does adding water to a saturated solution increase the number of ions present in the solution? In my book, it is stated that when some water is added to a test tube having a saturated $\ce{Ag2SO4}$ solution, with its solid at equilibrium, the number of $\ce{Ag}$ ions in the solution increases.

I don't understand it. If $\ce{Ag2SO4}$ solution is saturated, it means that no more solute can dissolve, and if we add water, the amount of dissolved solute should not change.

Also, if the amount of dissolved $\ce{Ag}$ increases, would the $K_\mathrm{sp}$ value also increase?
Consider a saturated solution of $\ce{Ag2SO4}$. The following equilibrium is attained.
$$ \ce{Ag2SO4 &lt;=&gt; 2Ag+  + SO4^2-}$$

Adding water accounts to increasing the volume of the solution. Hence more amount of solute can be dissolved since solubility of a salt depends on the amount of salt dissolved per unit volume. Therefore, there is an increase in the no. of ions produced in the solution. But as Avnish Kabaj mentioned, $[\ce{Ag+}]$ remains the same. 

Also as MollyCooL said, $\pu{K_{sp}}$ doesn't change as it is a constant at a particular temperature.