Abstract: Damodar river basin is repository of 40% of India coal reserve. Exploitation of coal and related industries in the area has exerted a great impact on the water pollution. In this study, an attempt has been made to develop a mathematical model to obtain time histories of concentration levels under different dumping policies so as to select the policy which disposes maximum waste without exceeding acceptable limits. An analytical solution is obtained to study the concentration levels for different time histories. The model can be useful in guiding engineering and management decision concerned with the efficient utilization of Damodar river water and protect their quality.