In an election, there were three candidates: A, B and C. 10% of the eligible voters did not vote. Out of those who voted, 45% voted for A, 35% voted for B and the remaining 20% voted for C. 30% of the votes polled for A and 20% of the votes polled for B were later deemed invalid, while all the votes polled for C were deemed valid. If A got 882 more valid votes than B did, how many valid votes did C receive?

5040

70% = \(\frac{7}{10}\) , 45% = \(\frac{9}{20}\)  , 90% = \(\frac{9}{10}\) , 80% = \(\frac{4}{5}\) , 35% = \(\frac{7}{20}\)

Let total valid votes = 100x

According to question ,

882 = Valid votes of A  - Valid votes of B

882 = ( 70% of 45% of 90% of 100x ) - ( 80% of 35% of 90% of 100x)

882 = ( \(\frac{7}{10}\) × \(\frac{9}{20}\) × \(\frac{9}{10}\) × 100x) - ( ( \(\frac{4}{5}\) × \(\frac{7}{20}\) × \(\frac{9}{10}\) × 100x)

882 = 28.35x - 25.2x

882 = 3.15x

x = 280

100x = 100 × 280 = 28000

So , total number of votes = 28,000