Question

$10\%$ of the voters did not cast their votes in an election between two candidates $10\%$ of the votes polled were found invalid. The successful candidate got $54\%$ of the valid votes and won by a margin of $1620$ votes. The number of voters enrolled in the voter's list was

• A. $25000$
• B. $33000$
• C. $35000$
• D. $40000$

Answer 1

Answer: (A)

$25000$

Let the total number of voters be $x.$

As $10\%$ of the voters did not cast their votes

Then, Votes polled $=90\%$ of $x.$

$10\%$ of the votes polled were found invalid
Valid votes $=90\%$ of $(90\%$ of $x)$.

$54\%$ of $[90\%$ of $(90\%$ of $x\left)\right]-46\%$ of $[90\%$ of $(90\%$ of $x\left)\right]=1620$

$=>8\%$ of $[90\%$ of $(90\%$ of $x\left)\right]=1620$

$\Rightarrow \frac{8}{100}\times \frac{90}{100}\times \frac{90}{100}\times x=1620$

$\Rightarrow x=\left(\frac{1620\times 100\times 100\times 100}{8\times 90\times 90}\right)=25000$