In an election between two candidates, 15% of the voters in the voters' list did not cast their votes and 10% of the votes polled were declared invalid. The winning candidate got 60% of the total valid votes and won by a majority of 7650 votes. The number of valid votes was :

Correct option is A

​$$\textbf{Given:} \\15\% \text{ voters did not vote} \\10\% \text{ votes were invalid} \\\text{Winning votes} = 60\% \text{ of valid votes} \\\text{Majority} = 7650 \\\textbf{Concept Used:} \\\text{Percentage and majority calculation} \\\textbf{Formula Used:} \\\text{Majority} = \text{Winning votes} - \text{Losing votes} \\\textbf{Solution:} \\\text{Votes cast} = 100\% - 15\% = 85\% \\\text{Invalid votes} = 10\% \text{ of } 85\% = 8.5\% \\\text{Valid votes} = 85\% - 8.5\% = 76.5\% \\\text{Let total voters} = N \\\text{Valid votes} = 0.765N \\\text{Winning votes} = 0.6 \times 0.765N = 0.459N \\\text{Losing votes} = 0.4 \times 0.765N = 0.306N \\\text{Majority} = 0.459N - 0.306N = 0.153N \\0.153N = 7650 \\N = 50000 \\\text{Valid votes} = 0.765 \times 50000 = 38250 \\\textbf{Final Answer:} \\38250$$​​