Question : Two candidates A and B contested in an election. 80% of the voters cast their votes, out of which 2% of the votes were invalid. A got 9,408 votes which was 60% of the valid votes. Find the total number of votes.
Option 1: 12,000
Option 2: 22,000
Option 3: 20,000
Option 4: 21,000
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Correct Answer: 20,000
Solution :
Let $x$ be the total number of votes.
Number of votes casted = 80% of $x$ = $\frac{80}{100}×x$
Number of invalid votes = 2% of votes cast
Number of valid votes = 98% of votes cast= $\frac{98}{100}×\frac{80}{100}×x$
Number of votes A got = 60% of valid votes
According to the question,
$\frac{60}{100}×\frac{98}{100}×\frac{80}{100}×x=9408$
⇒ $x=\frac{9408×100×100×100}{60×98×80}= 20000$
Hence, the correct answer is 20,000.
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