Question

in an election between two candidates 75% of the votes cast their vote out of which 2% votes are declared invalind . a canditate got 9261 votes which are 75% of the valid votes .the total number of votes in role in the election was

Answer 1

Solution :-

Let the total number of votes in role in the election be x

Votes cast = 75 %

⇒ 75 % of x

⇒ (x*75)/100 

Votes cast = 3x/4 

2 % of the votes cast were declared invalid.

⇒ 2 % of 3x/4

⇒ (3x*2)/(4*100)

⇒ 3x/200 

So, 3x/200 votes were declared invalid.

Total number of valid votes = 3x/4 - 3x/200

Taking LCM and then solving it.

⇒ (150x - 3x)/200

⇒ 147x/200

So, total number of valid votes were 147x/200

One of the candidates got 9261 which is 75 % of the valid votes.

⇒ 75 % of 147x/200 =  9261

⇒ (147x/200)*75/100

⇒ (147x*3)/(200*4) = 9261

⇒ 441x/800 = 9261

⇒ x = (9261*800)/441

⇒ x = 7408800/441

⇒ x = 16800

So, total number of votes in role in the election were 16800

Number of votes cast = (75*16800)/100 = 12600

Number of invalid votes = (12600*2)/100 = 252

Number of valid votes = 12600 - 252 = 12348

Answer.