Question

In an election between two candidates. 10%votes were invalid. first candidate got 1800 votes which were 60% of the valid votes. The total votes was?


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Answer 1

$\huge\tt\underline\red{Que}\underline {s}\underline\purple{tio}\underline{n}\orange {:}$

In an election between two candidates. 10%votes were invalid. first candidate got 1800 votes which were 60% of the valid votes. The total votes was?

$\huge\tt\underline\red{Ans}\underline {w}\underline\purple{er}\underline{:}\orange {10000}$

$\huge \underbrace \mathfrak \red{Explanation}$

$Let\: total\: number \:of\: votes \:be\: x$

$\large {\orange {Now ,}}$

$\boxed {A/q\: \: \: {1^{st}}}$

$\tt 10\%\: of \:votes\: were \:invalid$

$\tt \therefore \:The\: total \:number \:of \:voters\: = 90\%\: of \:x </p><p>[tex]\tt First \:candidate\: get\: 60\% \:vote\: = 60\%\: of\: ( 90\% of x )$

Then $\tt \boxed {A/q\: \: \: {2^{nd}}}$

$\tt 60\% of ( 90\% of x ) - 40\% of ( 90\% of x ) = 1800$

$\tt 20\% of ( 90\% of x ) = 1800$

$\tt \frac{20}{100} × \frac{90}{100} × x = 1800$

$\tt \frac{18}{100} × x = 1800$

$\tt x = \frac{1800×100}{18}$

$\tt x = \frac{\cancel {1800}×100}{\cancel{18}}$

$\tt \therefore x = 10000 \:\:\:\:\:\large {\green {\underline{ Ans}}}$