Cloud computing has been considered the new computing paradigm that would make the computing a utility. With the widespread acceptance of cloud computing, computing resources including computational power, storage, development platform and applications will be available as services. Hitherto computing resources were considered capital items and customers used to pay for these resources as for any other product. Cloud computing changes all these and consumers will pay only for what is consumed similar to other services or utilities. When cloud computing becomes more popular, different vendors would provide different services at different levels of qualities and prices. Hence customers will have to identify the differences in quality offered by different service providers and need to select the right service provider based on their requirements. A trust management system will match the service providers and the customers based on the requirements customers and the capabilities of service providers. In this paper, the authors propose a trust management system along with a trust evolution mechanism that can be used to measure the performance of services based on the response time of systems. The proposed mechanism formulates trust scores for different service level requirements based on assurance (confidence) levels. Hence this mechanism is suitable for managing multiple service levels against single trust score for all the service levels. Also the proposed mechanism is adaptive as it continuously modifies the scores based on the performance of the system. The proposed mechanism has been tested in a simulated environment and the results are found to be satisfactory.