Carrier Aggregation (CA) is one of the important features to support wider bandwidth for transmitting the packets in Long Term Evolution (LTE-A) Systems. Though there has been considerable work existing on Carrier Aggregation based packet scheduling, to the best of our knowledge the work regarding CA based LTE-A system packet scheduling considering service differentiation has not been investigated thoroughly till now. This paper focuses on packet scheduling using two methods, the first a conventional water filling method which does not consider service classes and the other one that considers the service class for packet aggregation. We consider downlink transmission which supports both Real-Time (RT) and non-Real-Time traffic simultaneously. Simulation results shows that while the water filling method indeed provides better performance in terms of delays in LTE system, the Service Class Based Carrier Aggregation(SCBCA) improves the throughput and provides better fairness among the service flows of different classes.