To solve the problem step by step, we will break down the information given and perform calculations accordingly.
### Step 1: Determine the Population of Each Village
The total population of villages A, B, and C is 80,000, and the ratio of their populations is given as 5:4:7.
Let the populations of villages A, B, and C be represented as:
- Population of A = 5x
- Population of B = 4x
- Population of C = 7x
The total population equation can be set up as:
\[ 5x + 4x + 7x = 80,000 \]
\[ 16x = 80,000 \]
Now, solve for x:
\[ x = \frac{80,000}{16} = 5,000 \]
Now, calculate the populations:
- Population of A = \( 5x = 5 \times 5,000 = 25,000 \)
- Population of B = \( 4x = 4 \times 5,000 = 20,000 \)
- Population of C = \( 7x = 7 \times 5,000 = 35,000 \)
### Step 2: Calculate the Number of Graduates in Village B
According to the problem, 36% of the population in village B are graduates.
Calculate the number of graduates in B:
\[ \text{Number of graduates in B} = 36\% \text{ of } 20,000 \]
\[ = \frac{36}{100} \times 20,000 = 7,200 \]
### Step 3: Determine the Male and Female Graduates
Let the number of female graduates be \( F \). According to the problem, the number of male graduates is 40% more than the number of female graduates.
Thus, the number of male graduates can be expressed as:
\[ M = F + 0.4F = 1.4F \]
Now, we can set up the equation:
\[ F + M = 7,200 \]
\[ F + 1.4F = 7,200 \]
\[ 2.4F = 7,200 \]
Now, solve for \( F \):
\[ F = \frac{7,200}{2.4} = 3,000 \]
### Step 4: Calculate the Percentage of Female Graduates in the Total Population
Now, we need to find out what percentage the number of female graduates (3,000) is of the total population of village B (20,000).
Calculate the percentage:
\[ \text{Percentage of female graduates} = \left( \frac{F}{\text{Total Population of B}} \right) \times 100 \]
\[ = \left( \frac{3,000}{20,000} \right) \times 100 \]
\[ = 15\% \]
### Final Answer
The percentage of female graduates in village B is **15%**.
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