Question : In an election between two candidates, the total number of votes polled was ' y '. 40 % of votes were invalid. The winning candidate got 60 % of the valid votes, while the other candidate lost by 6000 votes. Find the value of ' y '.
Option 1: 45000
Option 2: 50000
Option 3: 40000
Option 4: 30000
Correct Answer: 50000
Solution :
Total number of votes polled = $y$
Number of invalid votes = 40% of $y$ = $\frac{40y}{100}$ = $\frac{2y}{5}$
Number of valid votes = $1-\frac{2y}{5} = \frac{3y}{5}$
Votes of the winning candidate = 60% of $\frac{3y}{5} = \frac{60×3y}{100×5} = \frac{9y}{25}$
Votes of the lost candidate = 40% of $\frac{2y}{5} = \frac{40×3y}{100×5} = \frac{6y}{25}$
Lead = 6000
⇒ $\frac{9y}{25} - \frac{6y}{25}$ = 6000
⇒ $\frac{3y}{25}$ = 6000
⇒ $y = \frac{6000×25}{3}$
= 50000
Hence, the correct answer is 50000.
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