In a recent survey 25% houses contained two or more people. Of those houses containing only one person 20% were having only a male. What is percentage of all houses which contain exactly one female and no males?

Options

A. 0.55
B. 0.65
C. 0.6
D. 0.5

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the total number of houses
Let the total number of houses be \( X \).

### Step 2: Calculate the percentage of houses with one person
According to the problem, 25% of the houses contain two or more people. Therefore, the percentage of houses that contain only one person is:
\[ 100\% - 25\% = 75\% \]
So, the number of houses with one person is:
\[ \text{Houses with one person} = 75\% \text{ of } X = \frac{75}{100} \times X = \frac{3X}{4} \]

### Step 3: Determine the percentage of houses with only males
Out of the houses that contain only one person, 20% are males. Therefore, the number of houses with only males is:
\[ \text{Houses with only males} = 20\% \text{ of } \frac{3X}{4} = \frac{20}{100} \times \frac{3X}{4} = \frac{3X}{20} \]

### Step 4: Calculate the number of houses with only females
Since we know that the houses with only one person can either be males or females, we can find the number of houses with only females by subtracting the houses with only males from the total houses with one person:
\[ \text{Houses with only females} = \text{Houses with one person} - \text{Houses with only males} \]
\[ = \frac{3X}{4} - \frac{3X}{20} \]

### Step 5: Find a common denominator to simplify
To subtract these fractions, we need a common denominator. The least common multiple of 4 and 20 is 20. Therefore, we convert \(\frac{3X}{4}\) to have a denominator of 20:
\[ \frac{3X}{4} = \frac{15X}{20} \]
Now we can perform the subtraction:
\[ \text{Houses with only females} = \frac{15X}{20} - \frac{3X}{20} = \frac{12X}{20} = \frac{3X}{5} \]

### Step 6: Calculate the percentage of houses with exactly one female
To find the percentage of all houses that contain exactly one female, we divide the number of houses with only females by the total number of houses and multiply by 100:
\[ \text{Percentage of houses with only females} = \left(\frac{\frac{3X}{5}}{X}\right) \times 100 = \frac{3}{5} \times 100 = 60\% \]

### Final Answer
The percentage of all houses which contain exactly one female and no males is **60%**.

---