As far as I know, we can retrieve the WorkFlow rules by calling the metadata API. But my question here is, can we retrieve the WorkFlow rules by the object type. This is just to check how many Workflow rules available in the system for a specific object (Eg Case object). Is there any straight forward way to find these details?
Using Tooling API you can perform a SOQL query that will give you the number of Workflow Rules per object.
That query would be
SELECT count(Id), TableEnumOrId FROM WorkflowRule GROUP BY TableEnumOrId where TableEnumOrId will be the API Name of the sObject.