Question

in an election a candidate won by 25% of votes. if he secured 100 votes in excess of his opponent what are the total number of voters​

Answer 1

Given :

Extra percent of votes secured : 25%

Extra number of votes secured : 100

To find :

The total number of votes.

Solution :

Let the total number of votes be y.

Total number of votes :

According to the question,

$\sf \dashrightarrow 25\% \: of y = 100$

$\sf \dashrightarrow \dfrac{25}{100} \times y = 100$

$\sf \dashrightarrow \dfrac{1}{4} \times y = 100$

$\sf \dashrightarrow y = \dfrac{100 \times 4}{1}$

$\sf \dashrightarrow y = \dfrac{400}{1}$

$\sf \dashrightarrow y = 400$

Hence, the total number of votes were 400.

$\:$

Verification

$\sf \dashrightarrow 25\% \: of \: y = 100$

$\sf \dashrightarrow 25\% \: of \: 400 = 100$

$\sf \dashrightarrow \dfrac{25}{100} \times 400 = 100$

$\sf \dashrightarrow \dfrac{1}{4} \times 400 = 100$

$\sf \dashrightarrow \dfrac{1 \times 400}{4} = 100$

$\sf \dashrightarrow \dfrac{400}{4} = 100$

$\sf \dashrightarrow 100 = 100$

$\sf \dashrightarrow LHS = RHS$