You're right, but both have there own municipal corporation, which ever major cities of India have. below is the list
click hereIf we see Yadgiri is also having a municipal corporation, the district which divided from Kalburagi and if we club both population it is almost same as Solapur. Kalburagi(6 Lac) + Yadgiri (3.5 Lac) = Solapur (10 Lac).