Inan election only two candidates contested. 30% of the registered voter did not cast there votes and 180 votes were declared invalid. The winner got 684 votes more than his opponent. The number of valid votes received  by the winner is 42% of the number of registered voters. How many registered voters cast their votes?

Winner Valid Votes (W.V.V)

Winner Invalid Votes (W.I.V)

Loser Valid Votes (LVV)

Loser Invalid Votes (LIV)

Never Voted (N.V)

Total Votes

let total votes be 100x

then 

T.V = WVV+WIV+LVV+LIV+NV

(WIV+LIV = 180)

100X = 42X + 180+ 30X + LVV

In comparing the votes of loser and winner, the valid votes only be counted so, 

LVV = WVV - 684 = 42x-684

So, 

100X = 42X + 180 + 30X + 42X-684

X = 36

So, 100X = 3600,

So, Who voted = total - DN = 3600 - 30*36 = 2520

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