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
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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