qnli question: During waht centuries did the Western Chalukya rule? sentence: The Western Chalukya Empire (Kannada:ಪಶ್ಚಿಮ ಚಾಲುಕ್ಯ ಸಾಮ್ರಾಜ್ಯ) ruled most of the western Deccan, South India, between the 10th and 12th centuries.