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 contain exactly one female and no males?
(a) $15$
(b) $45$
(c) $75$
(d) Can’t be determined

Answer 1

Hint: For solving this problem, we will use the concept of percentage and form our equations as per the given data and solve further, to get the correct answer easily and select the correct option.

Complete step-by-step solution -
Given:
We have the following data from a recent survey:
1. $40\%$ houses contained two or more people
2. Of those houses containing only one person, $25\%$ were having only a male
Now, we have to find the percentage of all houses, which contain exactly one female and no males.
Now, let the total number of houses is $N$.
Before we proceed we should know that, what do we mean by $x\%$ of $N$.
Let us consider initially we have 100 number of pens.
Then, 1% of 100 $=\dfrac{1}{100}\times 100=1$ .
So, $x\%$ of $N=\dfrac{x}{100}\times N$.
Now, as it is given that $40\%$ houses contained two or more people. Then,
Number of houses contained two or more people $=\dfrac{40}{100}\times N=0.4N$ .
Now, we can easily find the number of houses containing only one person by subtracting the number of houses contained two or more people from the total number of houses. Then,
the number of houses containing only one person $=N-0.4N=0.6N$.
Now, as it is given that, of those houses containing only one person, $25\%$ were having only a male. Then,
Number of houses having only a male $=\dfrac{25}{100}\times 0.6N=0.15N$ .
Now, we can easily find the number of houses having only a female easily by subtracting the number of houses having only a male from the number of houses containing only one person. Then,
The number of houses having only a female $=0.6N-0.15N=0.45N$.
Now, we can find the percentage of all houses, which contain exactly one female and no males by dividing the number of houses having only a female by the total number of houses and then multiply it by $100$. Then,
The percentage of all houses, which contain exactly one female and no males $=\dfrac{0.45N}{N}\times 100=45$.
Thus, the required percentage is $45\%$.
Hence, (b) will be the correct option.

Note: Here, the student first should understand what is asked in the question and then proceed in the right direction to get the correct answer quickly. After that, we should apply the percentage concept carefully and proceed step by step to find the answer to the question. Moreover, calculations should be carried out carefully so that we can get the correct answer and avoid directly giving $\left( 100-25 \right)\%=75\%$ as the answer, it would be a wrong approach.