The result was announced by the District Returning Officer after the counting was over.
The by-poll was necessitated in Agar (Malwa) after sitting BJP MLA Manohar Untwal got elected as MP from Dewas Lok Sabha seat.
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Meanwhile, Congress which is striving hard to revive its fortunes in the state after remaining out of power since 2003, received some good news from Bahoriband seat in Katni district where its candidate Sourabh Singh is leading by a margin of 1,750 votes.
BJP had won the Bahoriband seat in the 2013 Assembly polls and by-poll was necessitated due to the death of sitting MLA Prabhat Pandey. The ruling party has fielded his son Pranav Pandey from the constituency.
In Vijaraghavgarh, BJP's Sanjay Pathak is leading by a margin of 17,000 votes against Congress' Brajendra Mishra.
Pathak had won the Vijayraghavgarh seat in 2013 from Congress with a thin margin. Later during Lok Sabha polls, he switched over to the BJP due to differences with the party leaders.
By-polls in these three constituencies, held last week witnessed a higher turnout of 69.98%, with Bahorband recording 71.80%, Agar 70.09% and Vijayraghavgarh 68.05%.