Question : Three candidates P, Q, and R participated in an election. P got 35% more votes than Q, and R got 15% more votes than Q. P overtook R by 2,412 votes. If 90% of voters voted and no invalid or illegal votes were cast, then what was the number of voters on the voting list?
Option 1: 46,900
Option 2: 42,800
Option 3: 42,210
Option 4: 48,500
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Correct Answer: 46,900
Solution : Let the total number of voters be $x$. Number of voters who cast their votes = 90% of the total number of voters = 0.9$x$ Let the number of votes for Q be $y$. The number of votes for P = 35% more votes than Q = 1.35$y$ Number of votes for R = 15% more votes than Q = 1.15$y$ Now, the difference between votes for P and R = 2412 So, 1.35$y$ – 1.15$y$ = 2412 ⇒ $y$ = 12060 Number of votes for P, Q, and R altogether = 1.35$y$ + $y$ + 1.15$y$ = 3.5$y$ Now, the number of votes for P, Q, and R altogether = Total number of votes cast ⇒ 3.5$y$ = 0.9$x$ ⇒ $x$ = $\frac{3.5\times 12060}{0.9}$ ⇒ $x$ = 46900 Hence, the correct answer is 46,900.
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