Question

In a election between two candidate 10% voters did not caste their vote and 2250 voter were found invalid and successful candidate got 54% of valid votes and won by majority of 1620 votes. What is the total number of voters in voter list.​

Answer 1

Let the total number of voters be x.

As 10% of the voters did not cast their votes

Then, Votes polled =90% of x.

10% of the votes polled were found invalid

Valid votes =90% of (90% of x).

54% of [90% of (90% of x)]−46% of [90% of (90% of x)]=1620

=>8% of [90% of (90% of x)]=1620

⇒

100

8

×

100

90

×

100

90

×x=1620

⇒x=(

8×90×90

1620×100×100×100

)=25000

Answer 2

Let the total number of voters be x.

As 10% of the voters did not cast their votes

Then, Votes polled =90% of x.

10% of the votes polled were found invalid

Valid votes =90% of (90% of x).

54% of [90% of (90% of x)]−46% of [90% of (90% of x)]=1620

=>8% of [90% of (90% of x)]=1620

$\implies \: \frac{8}{100} \times \frac{90}{100} \times \frac{90}{100} \times x = 1620$

$\small \bold{ \implies \: x = ( \frac{1620 \times 100 \times 100 \times 100}{8 \times 90 \times 90} ) = 25000}$