Question

If \[8\% \] of people eligible to vote are between 18 and 21 years of age. In an election, \[85\% \] of those eligible to vote, who were between 18 and 21 years, actually voted. In that election, the number of persons between 18 and 21, who actually voted, was what percent of those eligible to vote?
(a) \[4.2\]
(b) \[6.4\]
(c) \[6.8\]
(d) \[8.0\]

Answer 1

Hint: Here, first we will find the number of people eligible to vote (between 18 and 21 years). Then, we will find the number of people who actually voted (between 18 and 21 years). Finally, we will use the obtained expressions to calculate the required percentage.

Complete step-by-step answer:
Let the number of people eligible to vote be \[x\].
It is given that \[8\% \] of people eligible to vote are between 18 and 21 years of age.
Therefore, we get
Number of people eligible to vote (between 18 and 21 years) \[ = 8\% {\rm{ \,of\, }}x\]
Simplifying the expression, we get
Number of people eligible to vote (between 18 and 21 years) \[ = \dfrac{8}{{100}} \times x = \dfrac{{8x}}{{100}}\]
It is also given that \[85\% \] of those eligible to vote, who were between 18 and 21 years, actually voted.
This means that \[85\% \] of \[\dfrac{{8x}}{{100}}\] people actually voted.
Therefore, we get
Number of people eligible to vote (between 18 and 21 years) who actually voted \[ = 85\% {\rm{ \,of\, }}\dfrac{{8x}}{{100}}\]
Simplifying the expression, we get
Number of people eligible to vote (between 18 and 21 years) who actually voted \[ = \dfrac{{85}}{{100}} \times \dfrac{{8x}}{{100}} = \dfrac{{680x}}{{10000}}\]
Now, we will find the number of persons between 18 and 21, who actually voted as a percentage of the total number of people eligible to vote.
First, we will represent the number of persons between 18 and 21, who actually voted as a fraction of the total number of people eligible to vote.
Therefore, we get the fraction
$\Rightarrow$ \[\dfrac{{\dfrac{{680x}}{{10000}}}}{x} = \dfrac{{680}}{{10000}}\]
A fraction can be converted into a percentage by multiplying the fraction by 100.
Therefore, we can find the number of persons between 18 and 21, who actually voted as a percentage of the total number of people eligible to vote as
$\Rightarrow$ \[\dfrac{{680}}{{10000}} \times 100 = \dfrac{{680}}{{100}} = 6.8\% \]
Thus, we get the required percentage as \[6.8\% \].
Hence, the correct option is option (c).


Note: We used the terms ‘fraction’ and ‘percentage’ to find the solution.
A fraction is a number which represents a part of a group. It is written as \[\dfrac{a}{b}\], where \[a\] is called the numerator and \[b\] is called the denominator. The group is divided into \[b\] equal parts. The fraction \[\dfrac{a}{b}\] represents \[a\] out of \[b\] equal parts of the group.
A percentage is a number represented as a fraction with 100 as the denominator. It helps in comparing fractions with different denominators. Percent is represented by the symbol \[\% \].