<p>This paper considers the estimation of linear functions of scale parameters of two gamma distributions under an ordering between the scale parameters when the shape parameters are known. A class of estimators improving upon the restricted maximum likelihood estimators is proposed with respect to the squared error loss function. An inadmissibility result for estimating the linear functions of reciprocals of the scale parameters is also established. The percentage improvement of the proposed scale equivariant estimators compared to the existing estimators are shown through rigorous simulation procedures of Monte-Carlo. As an application, these estimators have been used to classify an observation into the considered gamma populations. When all parameters are unknown, the plug-in Bayes classification rules are proposed to classify observations into gamma populations using different estimators of the parameters. A likelihood ratio-based classification rule is derived to determine the class of the new observation. Finally, comparison among the proposed rules is carried out using simulations for known and unknown shape parameters. Two real-life data sets are analyzed to illustrate the performance of the classification rules.</p>