Using Ditkin's operator the exact analytical expressions for drawdowns for coupled two finite aquifer system in which pumpage from the upper and lower aquifer is balanced by a reduction in evapotranspiration from the upper aquifer are obtained. Also, the expressions for drawdowns for the limiting cases (viz. when the horizontal dimension of the aquifers is considered to be infinite) are deduced from one of the general results. It is observed that these results are the same as obtained by Motz. The application of Ditkin's operator in obtaining the solution for such problems is new and to our knowledge it has not been reported elsewhere in the literature.