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Question

In an election, two contestants $A$ and $B$ contested $x percent sign$ of the total voters voted for $A$ and $open parentheses x plus 20 close parentheses percent sign$ for $B.$ If 20% of the voters did not vote, then $x equals$

30
25
40
35

The correct answer is: 30

Let the total number of voters be $n$ . Then,
Number of voters voted for $A equals fraction numerator n x over denominator 100 end fraction$
Number of voters voted for $B equals fraction numerator n left parenthesis x plus 20 right parenthesis over denominator 100 end fraction$
$therefore$ Number of voters who voted for both
$equals fraction numerator n x over denominator 100 end fraction plus fraction numerator n left parenthesis x plus 20 right parenthesis over denominator 100 end fraction$
$equals fraction numerator n left parenthesis 2 x plus 20 right parenthesis over denominator 100 end fraction$
$H e n c e comma blank n minus fraction numerator n open parentheses 2 x plus 20 close parentheses over denominator 100 end fraction equals fraction numerator 20 n over denominator 100 end fraction rightwards double arrow x equals 30$

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