In a direct election between two contestants for the post

In a direct election between two contestants for the post of secretary, 4% of the total votes cast are declared to be illegal. One contestant secures 55% of the valid votes and wins with a majority of 240 votes, find the total number of votes cast.

Suppose total number of votes cast = x.
∴ Number of illegal votes = 4% of

x =	4x	=	x
	100		25

∴ Number of valid votes

= x –	x	=	25x - x	=	24x
	25		25		25

Votes secured by the contestant who is defeated

=	24x	–	24x	×	55
	25		25		100

=	24x			1 -	55
	25				100

=	24x	×	45
	25		100

According to the question,

=	24x	×	55	- 240
	25		100

=	24x	×	45
	25		100

⇒	24x			55	-	45		= 240
	25			100		100

⇒	24x	.	10	= 240
	25		100

=	24x	= 240
	250

⇒ x =	250 × 240	= 2500
	24

∴ Total number of votes cast = 2500