 QUESTION

# If ${\dfrac{2}{5}^{th}}$ of the votes promise to vote for P and rest promised to vote for Q. Of these on the last day 15% of the voters went back of their promise to vote for P and 25% of voters went back of their promise to vote for Q and P lost by 2 votes. Then the total number of voters is A. 100B. 110C. 90D. 95

Hint: Here, we will find the voters of P and Q then assume their values in the form of x. After forming the equation with the help of given information we will find the value of x and ultimately the total number of voters.

According to the question, ${\dfrac{2}{5}^{th}}$ of the voters promised to vote for P and the rest promised to vote for Q.
So, the rest voters who promised to vote for Q are $1 - \dfrac{2}{5} = \dfrac{3}{5}$
Let the total number of voters be 5x.
Then, voters of P = ${\dfrac{2}{5}^{th}}$ of 5x = 2x and
Voters of Q = 5x – 2x = 3x
On the last day 15% of the voters went back their promise to vote for P and 25% of voters went back of their promise to vote for Q which means they vote for P in spite of Q i.e.
2x – (15% of 2x) + (25% of 3x)
$\Rightarrow$2x – ($\dfrac{{15}}{{100}} \times$ 2x) + ($\dfrac{{25}}{{100}} \times$ 3x)
By simplifying it
$\Rightarrow$2x – 0.3x + 0.75x = 2.45x
Therefore, the total votes for Q = 5x – 2.45x = 2.55x
According to question, P lost by 2 votes i.e.
2.55x – 2.45x = 2
$\Rightarrow$0.1x = 2
$\Rightarrow$x = 20
Since, the total number of voters are 5x, so we will substitute the value of x in it
We get 5x = 5$\times$20 = 100 voters.
Hence, the total number of voters is 100.
Hence, the correct option is A.

Note: To find the total number of voters one should be able to understand the question and form the equations according to it. As you acknowledged the solution, you can see there is only this approach to these types of questions and to also avoid simple mistakes one must assume the given numbers as in variable form because it will be easy to evaluate the question and hence, get the result.