In an election held in a town, there were three candidates Arjun, Bhavesh, and Charan. Out of the total registered voters, 18% did not cast their votes. During counting, it was found that 6% of the votes polled were declared invalid. Among the valid votes, Arjun received 40% of the votes, while Bhavesh and Charan received the remaining valid votes in the ratio of 7 : 5, respectively. If Arjun won the election by 1,44,525 votes over Charan, then find the total number of registered voters in the town.

Let the total number of registered voters be $N$.

Votes polled $=82\%$ of $N$, and valid votes $=94\%$ of the votes polled. Hence, valid votes $=0.82\times0.94N=0.7708N$.

Arjun gets $40\%$ of the valid votes. The remaining $60\%$ is divided between Bhavesh and Charan in the ratio $7:5$, so Charan gets $\dfrac{5}{12}\times60\%=25\%$ of the valid votes.

Arjun's winning margin is $40\%-25\%=15\%$ of the valid votes.

$0.15\times0.7708N=144525$

$N=12,50,000$.