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 contain exactly one female and no males?
(a)15
(b)40
(c)75
(d)Cannot be determined
(e)None of these
Answer
Answer (as printed): E
Explanation
Let the total number of houses be $x$. Then, Number of houses having one female only $=(100-25) \%$ of $(100-40) \%$ of $x=\left(\frac{75}{100} \times \frac{60}{100} \times x\right)=\frac{9}{20} x$. $$\text { ∴ } \text { Required percentage }=\left(\frac{9 x}{20} \times \frac{1}{x} \times 100\right) \%=45 \% .$$
Explanation as extracted from the printed page; notation may be imperfect.