With the growing number of wireless and mobile devices ingrained into our daily lives, more and more people are interacting with online services that adopt recommender systems to suggest movies, news and points of interest. The private demographics of users such as age and gender in online recommender systems are very useful for many applications such as personalized ads, social study and marketing. However, users do not always provide details in their online profiles due to privacy concern. Most existing approaches can infer user private attributes based on sufficient interaction history but could fail for new users with few ratings. In this paper, we present a novel preference elicitation method, with which a recommender system asks cold-start users to rate selected items adaptively and infer the demographics rapidly via a few interactions. Specifically, latent user profiles are learned across the tasks of demographic inference and rating prediction simultaneously, which enables knowledge transfer through the two related tasks and improves the prediction accuracy for both tasks. The proposed method can also facilitate the understanding of the tradeoff between user privacy and the utility of personalization. Experimental results on real-world datasets demonstrate the performance of the proposed method in terms of the accuracy of both demographics inference and rating prediction.