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In an election between two candidates, 80% of the registered voters cast their votes. Out of these, 2% were declared invalid. One candidate secured 8,
Question

In an election between two candidates, 80% of the registered voters cast their votes. Out of these, 2% were declared invalid. One candidate secured 8,820 votes, which accounted for 75% of the valid votes. Find the total number of registered voters.

A.

16,200

B.

15,800

C.

15,200

D.

15,000

Correct option is D

Given
Registered voters who cast votes = 80%
Invalid votes = 2% of cast votes
Candidate secured = 8820 votes (75% of valid votes)
Formula Used
​Total Value=Given PartPercentage×100\text{Total Value} = \frac{\text{Given Part}}{\text{Percentage}} × 100​​
Solution
Let the total valid votes be V.
​75% of V=8820V=8820×10075=1176075\% \text{ of } V = 8820\\V = 8820 × \frac{100}{75} = 11760​​
Let the total votes cast be C.
Since 2% were invalid, 98% of the cast votes are valid.
​98% of C=11760C=11760×10098=1200098\% \text{ of } C = 11760\\C = 11760 × \frac{100}{98} = 12000​​
Let the total registered voters be R.
Since 80% of registered voters cast their votes:
​80% of R=12000R=12000×10080=1500080\% \text{ of } R = 12000 \\R = 12000 × \frac{100}{80} = 15000​​
Final Answer
So the correct answer is (d)

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