Knowledge about the hemodynamic model that mediates synaptic activity and measured magnetic resonance signal is essential in understanding brain activation. Neural efficacy is a hemodynamic parameter that would change the evoked hemodynamic responses. In this work, brain activation and neural efficacy of the activated brain areas during simple addition task in two different backgrounds were studied using fMRI. The objectives were to determine the activated areas during the performance of arithmetic addition in quiet (AIQ) and noisy (AIN) background and to investigate the relationship between neural efficacy and height extent of activation for the respective areas. Eighteen healthy male participants performed simple arithmetic addition in quiet and in noise. Bilateral cerebellum, superior temporal gyrus (STG), temporal pole (TP) and supplementary motor area (SMA) were significantly (p < 0.05) activated during AIQ and AIN. Left middle frontal gyrus (L-MFG), right superior frontal gyrus (R-SFG), right superior orbital gyrus (R-SOG) and bilateral insula were more active in quiet as compared to in noise while the left middle cingulate cortex (L-MCC), left amygdala (L-AMG), right temporal pole (R-TP) and left cerebellum (L-CER) were more active in noise as compared to in quiet. The t value for most of the activated regions was found to be inversely proportional to the neural efficacy. Significant (p < 0.05) negative relationship between t value and neural efficacy were found for R-STG and bilateral cerebellum during AIQ, while for AIN, similar relationships were found in R-CER, R-STG and R-TP. This study suggests that while being significantly activated, the hemodynamic responses of these brain regions could have been suppressed by the stimulus resulting in an intensity decrease with increasing neural efficacy.