Question

In a recent survey, \[40\% \] houses contained two or more people of those houses containing only one person \[25\% \] were having only a male what is the percentage of all houses which contains exactly one female and no males -
(A)\[15\] (B) \[45\] (C) \[75\] (D) cannot be determined

Answer 1

Hint: – Here we have to find the problem by percentage concept..here we have to use all the possibilities to solve the problem..when we find all the possibilities then we can easily say about the appropriate answer.


Complete step by step solution:
Number of houses with only one female \[ = \left( {100 - 25} \right)\% \] of $\left( {100 - 40} \right)\% {\text{ of }}x$.
Where \[x\] denotes the no of family present there.
Therefore,
Female \[ = \left( {100 - 25} \right)\% \] of $\left( {100 - 40} \right)\% {\text{ of }}x$
$
  75/100 \times 60/100 \times x \\
  3/4 \times 3/5 \times x \Rightarrow 9x/20 \\
 $
Required problem based on the maximum percentage of family \[ = {\text{ }}\% \] $\frac{{9x}}{{20}} \times \frac{1}{x} \times 100 \Rightarrow 45$
Then option \[\left( B \right)\] is correct in this question.


Note: - When solving problems like these ,make sure to consider the percentage appropriately and also if it is give in proportions ,make sure to convert the proportions into percentage and then find the answer