Question : 2 candidates contested an election. The winning candidate got 52% of the valid votes and won by a margin of 360 votes. If 10% of votes were declared invalid, then what was the total number of votes polled?
Option 1: 11,000
Option 2: 10,000
Option 3: 8,000
Option 4: 12,000
Correct Answer: 10,000
Solution :
The winning candidate received 52% of the valid votes.
The winning candidate won by a margin of = 360 votes.
Percent of the votes were declared invalid = 10%
Let the total number of votes polled be denoted as "T"
Let the number of valid votes be denoted as "V" = 90% of T
Let the number of votes received by the winning candidate be denoted as "W" = 52% of V
Let the number of votes received by the losing candidate be denoted as "L" = 48% of V
$\because$ The winning candidate won by a margin of 360 votes, we have:
Substituting the values of W and L in the equation W - L = 360, we get:
= $(\frac{52}{100}) \times \text{V} - (\frac{48}{100}) \times \text{V} = 360$
Simplifying the above equation, we get:
⇒ $(\frac{4}{100}) \times \text{V}$ = 360
⇒ V = $\frac{360 \times 100}{4}$
⇒ V = 9000
Therefore, the total number of votes polled is:
T = $\frac{\text{V}}{0.9}$ (since valid votes are 90% of total votes)
⇒ T = $\frac{9000}{0.9}$
⇒ T = 10000
$\therefore$ The total number of votes polled is 10,000.
Hence, the correct answer is 10,000.
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