It is quite difficult to manage and optimize websites for desktops and several mobile devices and produce optimal results. And, for that you should know, Google recommends RWD as a great way to optimize websites for mobile devices and target mobile users. Google favors mobile-optimized sites and thus, produce better results for searches made on a mobile device.
Optimizing your site makes it easier for visitors to browse through the content of the website. User experience is a tremendous ranking factor that can attract as well as distract your audience. A responsive website automatically adapts to the screen while presenting the content in an easy to browse format and providing a mobile-friendly experience to mobile users.
Of course, it takes less time to create a single website that suits the needs of all the users and devices than to create two different sites optimized for two different user platforms (mobile devices and desktops). A responsive website consumes less time and money as maintenance and upgrades need to be applied to one place. The modifications and functionality you apply to the desktop version of the website are automatically applied to the mobile version as well.
Any visitor who has a hard time browsing through your website and finding what they are looking for is more likely to leave the website and visit your competitor websites. A RWD presents the relevant information in a functional and well-organized way that helps visitors stay engaged and do not visit other websites.