The complete and incomplete fusion cross sections for $^{7}$Li+$^{124}$Sn reaction were measured using online and offline characteristic $gamma$-ray detection techniques. The complete fusion (CF) cross sections at energies above the Coulomb barrier were found to be suppressed by $sim$ 26 % compared to the coupled channel calculations. This suppression observed in complete fusion cross sections is found to be commensurate with the measured total incomplete fusion (ICF) cross sections. There is a distinct feature observed in the ICF cross sections, i.e., $textit{t}$-capture is found to be dominant than $alpha$-capture at all the measured energies. A simultaneous explanation of complete, incomplete and total fusion (TF) data was also obtained from the calculations based on Continuum Discretized Coupled Channel method with short range imaginary potentials. The cross section ratios of CF/TF and ICF/TF obtained from the data as well as the calculations showed the dominance of ICF at below barrier energies and CF at above barrier energies.
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