In this paper, we propose a method for incremental learning of two distinct tasks over time: acoustic scene classification (ASC) and audio tagging (AT). We use a simple convolutional neural network (CNN) model as an incremental learner to solve the tasks. Generally, incremental learning methods catastrophically forget the previous task when sequentially trained on a new task. To alleviate this problem, we use independent learning and knowledge distillation (KD) between the timesteps in learning. Experiments are performed on TUT 2016/2017 dataset, containing 4 acoustic scene classes and 25 sound event classes. The proposed incremental learner solves the AT task with an F1 score of 54.4% and the ASC task with an accuracy of 88.9% in an incremental time step, outperforming a multi-task system which solves ASC and AT at the same time. The ASC task performance degrades only by 5.1% from the initial time ASC accuracy of 94.0%.