The reaction $$X \to Y$$  is an exothermic reaction. Activation energy of the reaction for $$X$$ into $$Y$$ is $$150\,kJ\,mo{l^{ - 1}}.$$   Enthalpy of reaction is $$135\,kJ\,mo{l^{ - 1}}.$$   The activation energy for the reverse reaction, $$Y \to X$$  will be :

Solution :
$$\eqalign{ & X \to Y;\Delta H = - 135\,kJ/mol, \cr & {E_a} = 150\,kJ/mol \cr & {\text{For an exothermic reaction}} \cr & {E_{a\left( {F.R} \right)}} = \Delta H + E{'_{a\left( {B.R.} \right)}} \cr & 150 = - 135 + E{'_{a\left( {B.R.} \right)}} \cr & E{'_{a\left( {B.R.} \right)}} = 285\,kJ/mol \cr} $$