How to calculate the new concentration of a solution after adding more solute and convert it to ppm?
Let's think about it :

You have the formula of the mass concentration $C_m$: 

$C_m = \frac{m}{V}$, 

where $m$ is the mass in grams of solute and $V$ the volume in liters of the solution. 

A first step for you would be to calculate the mass of solute already in the solution : your solution has a volume of $0.5~\mathrm m^3$, which is $V=500~\mathrm L$, with a massic concentration of $C_m=10~\mathrm{mg\cdot L^{-1}}$. Therefore, there is already a mass 

$m=C_m~\times~V = 10\cdot10^{-3} \times 500 = 5~\mathrm g$ 

of salt in your solution. 

To this mass, you add $2~\mathrm g$ of salt, so the mass of solute in your solution is now $m=5~\mathrm g + 2~\mathrm g = 7~\mathrm g$.

So, at end you have a mass $m=7~\mathrm g$ of salt. 

I let you compute the mass of solution, knowing that $1~\mathrm L$ of water weights $1~\mathrm{kg}$.