In a village two-third are male and remaining are female. `80%` of male and `70%` of female are literate. `40%` of lierate male and `30%` of literate female are graduate . `12(1)/(2)%` of graduate male and `14(2)/(7)%` of graduate female have a government job. Find the percentage of people who have government job to the total number of people in the village.

Options

A. `600%`
B. `(11)/(3)%`
C. `(45)/(9)%`
D. `700%`

Answer

To solve the problem step by step, we will break down the information given and calculate the required values systematically.

### Step 1: Determine the Total Population of the Village
Let the total population of the village be \( P \).

### Step 2: Calculate the Number of Males and Females
According to the problem:
- Two-thirds of the population are male.
- One-third of the population are female.

So, we can express the number of males and females as:
- Number of males = \( \frac{2}{3}P \)
- Number of females = \( \frac{1}{3}P \)

### Step 3: Calculate the Number of Literate Males and Females
From the problem:
- \( 80\% \) of males are literate.
- \( 70\% \) of females are literate.

Calculating the number of literate males and females:
- Literate males = \( 0.8 \times \frac{2}{3}P = \frac{16}{30}P \)
- Literate females = \( 0.7 \times \frac{1}{3}P = \frac{7}{30}P \)

### Step 4: Calculate the Number of Graduate Males and Females
From the problem:
- \( 40\% \) of literate males are graduates.
- \( 30\% \) of literate females are graduates.

Calculating the number of graduate males and females:
- Graduate males = \( 0.4 \times \frac{16}{30}P = \frac{64}{300}P \)
- Graduate females = \( 0.3 \times \frac{7}{30}P = \frac{21}{300}P \)

### Step 5: Calculate the Number of Graduate Males and Females with Government Jobs
From the problem:
- \( 12.5\% \) of graduate males have a government job.
- \( 14.2857\% \) (which is \( \frac{14}{7} \) or \( 14 \frac{2}{7}\% \)) of graduate females have a government job.

Calculating the number of graduate males and females with government jobs:
- Government job males = \( 0.125 \times \frac{64}{300}P = \frac{8}{300}P \)
- Government job females = \( \frac{14.2857}{100} \times \frac{21}{300}P = \frac{3}{300}P \)

### Step 6: Calculate the Total Number of People with Government Jobs
Total with government jobs = Government job males + Government job females:
\[ \text{Total with government jobs} = \frac{8}{300}P + \frac{3}{300}P = \frac{11}{300}P \]

### Step 7: Calculate the Percentage of People with Government Jobs to the Total Population
To find the percentage of people who have government jobs:
\[ \text{Percentage} = \left( \frac{\text{Total with government jobs}}{P} \right) \times 100 = \left( \frac{\frac{11}{300}P}{P} \right) \times 100 = \frac{11}{300} \times 100 = 3.67\% \]

### Final Answer
The percentage of people who have government jobs to the total number of people in the village is approximately **3.67%**.

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