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In an election there were two candidates A and B, 20% of voters did not vote, 10% of polled votes were declared invalid. A received 50% votes of polling and won by 600 votes .What was the total number of voters?

Answer:

Explanation:

Let the total no. of voters be $= x$

No of voters polled $= 80$% of $x = \frac{4x}{5}$

Invalid votes $= 10$% of $\frac{4x}{5}$ $= \left(\frac{10}{100}\right)\times \left(\frac{4x}{5}\right)$

$ = \frac{2x}{25}$

Valid votes  $= \left(\frac{4x}{5}\right)-\left(\frac{2x}{25}\right)$ $=\frac{18x}{25}$

Votes received by $A = 50$% of $\frac{4x}{5}$ $=\left(\frac{50}{100}\right)\times \left(\frac{4x}{5}\right)$

$= \frac{2x}{5}$

Votes received by $B = \left(\frac{18x}{25}\right)-\left(\frac{2x}{5}\right)$ $=\frac{8x}{25}$

Given, $\left(\frac{2x}{5}\right)-\left(\frac{8x}{25}\right) = 600$

$\therefore$ $\frac{2x}{25}= 600$

$\therefore$ $x = \frac{(600\times 25)}{2}$

$= 7500$