Question

In an election between two candidates, 30% of the voters didn't cast their vote, 500 votes were declared as invalid, the winner got 60% of the valid votes, and won by a margin of 2000 votes. find the total number of votes in the voting list.
1. 20000
2. 17000
3. 16000
4. 14000
5. 15000

Answer 1

Correct Answer - Option 5 : 15000

GIVEN:

% of voters who didn't cast their vote = 30%

invalid votes = 500

winner's share = 60% of valid votes 

margin = 2000 votes

EXPLANATION:

let the total number of voters on the list be x

\(votes \space polled = 70\%\space of \space x\Rightarrow\frac{7}{10}\times x \\valid \space votes = \frac{7}{10}\times x - 500 \\winner's\space share =60\%\\loser's \space share = 40\% \\margin = 20\%\space of \space valid\space vote s \\\therefore\frac15\times[\frac{7}{10}\times x- 500]=2000 \\\Rightarrow x=15000\)

ALTERNATE SOLUTION:

let valid votes be 100

\(margin= 20\%\space of \space valid\space votes =2000 \\total\space valid\space votes =10000 \\votes\space polled =10000+500=10500 \\votes \space polled = 70\%\space of \space list \\\Rightarrow70\%=10500 \\\Rightarrow100\%=\frac{10500}{70}\times100=15000\)