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❍ Question :-


✰ $At\:an\:election\: between\: two\: candidates\:53\:votes\:were\:declared\:invalid.\:The\:winning\: candidate\:secures\:58\%\:of \:the\:valid\:votes\:and \:wins\: by\: 588 \:votes .\: Find \:the \:total\: no. \:of \:votes \:polled. \:$

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Answer 1

Answer:

Answer is in attachment hope it helps you ✌✌

Answer 2

$\Large ✰ \: \: \underline \boldsymbol{\: Topic \: \: \: ➠ \: \: \: \frak {Percentage}}.$

$\Large ✰ \: \: \underline \boldsymbol{\: Question }\: \: \: \downarrow \downarrow\downarrow \\ \:$

$\: \: \: \: \begin{cases} \rm \: At\:an\:election\: between\: two\: candidates\\ \rm53\:votes\:were\:declared\:invalid.\:The\:winning\\ \rm \: candidate\:secures\:58\%\:of \:the\:valid\:votes\:and \\ \rm \: wins\: by\: 588 \:votes .\: Find \:the \:total\: no. \:of \:votes \:polled. \end{cases}$

$\Large ✰ \: \: \underline \boldsymbol{ Solution} \: \: \: \downarrow\downarrow\downarrow$

$\frak{❃ \:\;Given } \: - \begin{cases} \tt \: \underline{Let \: the \: total \: no. \: of \: valid \: votes \: \bf x} \\ \tt\underline{ \: Percentage \: of \: valid \: votes \: secured \: by \: winning \: candidates \: = \bf\: 58 \%} \: \\ \tt \underline{\: Percentage \: of \: valid \: votes \: secured \: by \:defeated \: candidates \: = \bf \: (100 - 58 )\% = 42\% }\\ \tt \underline{\: Difference \: between \: their \: votes \: = \bf\: 588. } \end{cases}$

$\tt\therefore \: (58 \% \: of \: x) - (42\% \: of \: x) \: = \: 588 \\ \\ : \tt \implies \: \bigg( \frac{58}{100} \times x\bigg) - \bigg( \frac{42}{100} \times x \bigg) \: = \: 588 \\ \\ \tt : \implies \: \bigg( \frac{58x}{100} - \frac{42x}{100} \bigg) = \: 588 \\ \\ \tt : \implies \: \frac{(58x - 42x)}{100} = \: 588 \\ \\ \tt : \implies \: 16 \: x \: = \: 588 \times 100 \\ \\ : \implies\tt x \: = \: \tt\frac{588 \times 100}{16} \\ \\ : \implies \underline {\boxed{\frak {x \: = \: 3675.}}}$

$\tt \: \underline { \therefore \: No. \: of \: valid \: votes \: = \: 3675 \: and \: no. \: of \: valid \: votes \: = \: 53.}$

$\boldsymbol {\underline{{✠\;\:Hence}, \: \tt \: the \: total \: no. \: of \: votes \: polled \: = \: \bf (3675 + 53) = 3728.}}$

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