Question

In an election survey, 30% people promised to vote candidate A and remaining promised to vote for candidate B. If on the day of election x% of people who promised to vote for A, voted for B and 40% of people who promised to vote for B voted against him and in the end B lost by 10 votes. What is value of x, if total 250 votes were?
(Please Solve it) ​

Answer 1

Total votes = 250

Votes promised to A = $30\%\ of\ 250$

$\Rightarrow 75$

Votes promised to B = 250 - 75

$\Rightarrow 175$

According to the question, $40\%$ of the votes promised to B were given to A.

$40\%\ of\ 175 = \dfrac{40}{100} \times 175 = 70$

i.e. 70 votes promised to B were actually given to A.

and $x\%$ of votes promised to A were given to B.

i.e. $\dfrac{x}{100}\times 75$

$\Rightarrow \text{Actual votes to A} = \text{Number of Votes promised to A} - \\ \text{Number of Votes promised to A but actually given to B} + \\ \text{Number of Votes promised to B but actually given to A}$

$\Rightarrow 75 - \dfrac{x}{100}\times 75 + 70\\\Rightarrow 145 - \dfrac{x}{100}\times 75\\\text{Actual votes to A} = 145 - \dfrac{3}{4} \times x ....... (1)$

$\text{Actual votes to B} = \text{Number of Votes promised to B} - \\\text{Number of Votes promised to B but actually given to A} + \\\text{ Number of Votes promised to A but actually given to B}$

$\Rightarrow 175 - 70 + \dfrac{x}{100}\times 75\\\text{Actual votes to B} = 105 + \dfrac{3}{4} \times x ....... (2)$

Now, as per question, B lost by 10 votes

Subtracting equation (2) from equation (1):

$\Rightarrow 145 - \dfrac{3}{4} \times x - (105 + \dfrac{3}{4} \times x) = 10\\\Rightarrow 40 - 2 \times \dfrac{3}{4} \times x = 10\\\Rightarrow \dfrac{3}{2} \times x = 30\\\Rightarrow x = 20 \%$

Hence, value of $x$ is $20\%$.