Image super-resolution and denoising are two important tasks in image processing that can lead to improvement in image quality. Image super-resolution is the task of mapping a low resolution image to a high resolution image whereas denoising is the task of learning a clean image from a noisy input. We propose and train a single deep learning network that we term as SuRDCNN (super-resolution and denoising convolutional neural network), to perform these two tasks simultaneously . Our model nearly replicates the architecture of existing state-of-the-art deep learning models for super-resolution and denoising. We use the proven strategy of residual learning, as supported by state-of-the-art networks in this domain. Our trained SuRDCNN is capable of super-resolving image in the presence of Gaussian noise, Poisson noise or any random combination of both of these noises.