For the reaction $A_2 + B_2 \rightleftharpoons 2AB$,the activation energies for the forward and backward reactions are $180 \, kJ \, mol^{-1}$ and $200 \, kJ \, mol^{-1}$ respectively. In the presence of a catalyst,the activation energy for both (forward and backward) reactions decreases by $100 \, kJ \, mol^{-1}$. What will be the enthalpy change $(\Delta H)$ for the reaction $(A_2 + B_2 \rightarrow 2AB)$ in the presence of a catalyst in $kJ \, mol^{-1}$?

• A
  $300$
• B
  $120$
• C
  $280$
• D
  $-20$