Cloud computing emerges as a hottest trend in area of information technology and heterogeneous networking. Due to less efficient allocation resources in a cost-efficient cloud environment, a user can tolerate a certain degree of delay while retrieving information from the cloud to reduce costs. In this paper, we focused on two primary issues in such an environment: search privacy and efficiency. We first come across a private searching scheme that was originally proposed by Ostrovsky. Their private keyword based retrieval scheme allows a user to retrieve files of interest from un-trusted servers in leakage of any information. The main drawback is because of processing of all the queries from different users, it will cause a heavy querying overhead incurred on the cloud and thus goes against the original intention of cost efficiency. In this paper, we present three efficient information retrieval for ranked query (EIRQ) schemes to reduce querying overhead incurred on the cloud. In EIRQ, queries are classified into multiple ranks, where a higher ranked query can recover a higher percentage of matched files on user demand. A user can retrieve files on demand by choosing queries of different ranks. This feature is useful when the user only needs a small subset of files from large number of matched files. This system introduces retrieval of files with low bandwidth and low computational and communication cost. Under different parameter settings, extensive evaluations have been conducted on both analytical models and on a real cloud environment, in order to examine the effectiveness of our schemes.