Different cuts of beef do require slightly different roasting times. The size of the roast and the temperature desired in the roast are far more important factors, however.
An eye of round roast takes longer to cook than a round tip roast and both of these roasts take longer to cook than a sirloin tip roast or a tenderloin. Also, any roasts that are bone-in typically take longer to cook than roasts that are boneless. All times when cooking beef though are approximations, because they are altered by the size of the cut. A 3 pound roast will always take longer to cook than a 2 pound roast.
The best way to cook perfect roasts is with the use of a meat thermometer rather than by timing them, as a meat thermometer is more precise. Cooking a roast to an internal temperature of 125 degrees will produce a roast that is rare, while 135 degrees is medium rare, 150 degrees is medium, 155 degrees is medium well and anything over 160 degrees is well done. These temperatures are the same for almost every cut of beef. It is also always beneficial, when taking a roast out of the oven, to give it roughly 15 minutes to rest before slicing it.