In an election between two candidates, A and B, 18% of total voters did not cast their votes. 15% of the votes polled were declared invalid. B received 56% of the total valid votes and won by a majority of 6273 votes. The number of valid votes received by A was:

Let the total number of registered voters = $V$

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People who actually voted:

$100\% - 18\% = 82\%$ of total voters

Votes polled = $0.82V$

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Valid votes from the polled votes:

$100\% - 15\% = 85\%$ of polled votes

Valid votes = $0.85 \times 0.82V = 0.697V$

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Votes received by each candidate:

B received $56\%$ of valid votes = $0.56 \times 0.697V = 0.39032V$

A received remaining valid votes = $44\%$ of valid votes = $0.44 \times 0.697V = 0.30668V$

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Using the majority information:

B won by $6273$ votes, so:

$0.39032V - 0.30668V = 6273$

$0.08364V = 6273$

$V = \dfrac{6273}{0.08364} = 75000$

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Valid votes received by A:

A's votes $= 0.30668 \times 75000 = 23001$

Therefore, A received $23001$ valid votes.