Question

In a recent survey, \[25%\] contained two or more people. Of those houses containing only one person \[20%\] were having only a male. What is the percentage of all houses which contain exactly one female and no males?
\[
 \left( A \right)55% \\
 \left( B \right)65% \\
 \left( C \right)60% \\
 \left( D \right)50% \\
\]

Answer 1

Hint: This question can be solved by considering the total number of houses \[x\] and as it is given that the \[25%\] contain more than one person, so we estimate the value of \[75%\] of \[x\] and then after finding the percentage of single females we multiply it by the number of houses that contain one single person.

Formula used: The percentage of a number is expressed as:
\[x%=\dfrac{x}{100}\]
And
\[x% of y=\dfrac{x}{100}\times y\]

Complete step-by-step solution:
Firstly let us assume the total number of the houses
Let the number of houses \[=x\]
Now, since, it is given that \[25%\] of these houses contain more than one person,
Then, the remaining houses contain only one. Thus, \[\left( 100-25 \right)%=75%\] of the houses contain a single person
\[\therefore x\times \dfrac{75}{100}=\dfrac{3x}{4}\]
Now, we have the number of houses that contain one single person,
And it is given that \[20%\] of these houses are the ones that contain only single male.
Therefore, the remaining percentage is that of the houses that contain single females. So, we can find the percentage of all the single females by:
\[
 \Rightarrow \left( 100-20 \right)%=80% \\
\Rightarrow \dfrac{80}{100}\times \dfrac{3x}{4} \\
 \Rightarrow \dfrac{60x}{100} \\
 \Rightarrow 60%ofx \\
\]
Hence, the total percentage of houses that contain single females is \[60%\].

Thus, option \[\left( C \right)60%\] is the correct answer.

Note: In this we have been given the percentages of the things and we had to find that of the opposite case, so we found the required number of houses by subtracting the given conditions from \[100%\]and estimate the required number of houses.