Assam saw 82.02 per cent voting in its second and final phase of Assembly elections while 79.51 per cent polling was reported in part two of the first phase of polls in West Bengal on Monday. The Election Commission said polling in the two states was "very peaceful."
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Deputy Election Commissioner Sandeep Saxena said there was "no violence, injury or death" inside any polling station in the two states.
In West Bengal, there was information of "sporadic" clashes between workers of different political parties.
More than 800 complaints were received by the Election Commission in West Bengal over issues like polling agents not being allowed to enter booths.
The Trinamool Congress is hoping for a second term in Bengal. A big fight is expected at Asansol, where the BJP won one of its two seats in the 2014 general elections. There was tension at the Sabang seat where a local Trinamool leader was beaten to death on Friday.
For Assam, this phase is crucial in view of the minority vote. Of the 61 seats that voted, the Muslim vote would be a determining factor in more than 30 seats, where perfume baron and AIUDF chief Badruddin Ajmal directly clashed with the Congress. In 2011, Mr Ajmal won 18 seats and became the main opposition party in the state.
With identity politics playing a major role in these areas, the BJP has accused the Congress of allowing infiltration from neighbouring Bangladesh over the last 15 years to shore up the party's vote bank. The Congress has denied the change.
Today's polls in Assam are key for the BJP, which is hoping to wrest power in the state. Among the districts going to polls are Kokrajhar and other Bodo districts in lower Assam, where the party is hoping to win a chunk of seats.
Prime Minister Narendra Modi has led a high-voltage BJP campaign in Assam, taking on not only Chief Minister Tarun Gogoi, but also Sonia and Rahul Gandhi, who head Congress. At one rally, PM Modi said Chief Minister Gogoi, who will be 90 soon, should consider retirement. Mr Gogoi, who is 81, has said the PM had wounded the Assamese pride.
Last week, Mamata Banerjee and Narendra Modi had crossed swords at Asansol. The war of words had placed both under the scanner of the Election Commission.
BJP has targeted the Trinamool government over the Saradha ponzi scam, the Narada sting operations, in which several party leaders were allegedly caught on camera while accepting bribes and the Kolkata flyover collapse.