In a village `(2)/(3)` are males and rest are females. `80%` of males and `70%` of females are literate. `50%` of literate males and `40%` of literate females are graduates. `20%` of graduate males and `28(4)/(7)%` of graduate females are in a government job. Find the no. of males and females are in government service is what `%` of total population of the village.

Options

A. `8%`
B. `3%`
C. `9.5%`
D. `1%`

Answer

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

### Step 1: Determine the total population and the number of males and females.
Given that \( \frac{2}{3} \) of the population are males, the remaining \( \frac{1}{3} \) are females.

Let the total population be \( P \).

- Number of males = \( \frac{2}{3}P \)
- Number of females = \( \frac{1}{3}P \)

### Step 2: Calculate the number of literate males and females.
According to the problem:
- \( 80\% \) of males are literate.
- \( 70\% \) of females are literate.

Calculating the literate males:
- Literate males = \( 80\% \) of \( \frac{2}{3}P = 0.8 \times \frac{2}{3}P = \frac{16}{30}P = \frac{8}{15}P \)

Calculating the literate females:
- Literate females = \( 70\% \) of \( \frac{1}{3}P = 0.7 \times \frac{1}{3}P = \frac{7}{30}P \)

### Step 3: Calculate the number of graduates among literate males and females.
According to the problem:
- \( 50\% \) of literate males are graduates.
- \( 40\% \) of literate females are graduates.

Calculating the graduates among literate males:
- Graduates (males) = \( 50\% \) of \( \frac{8}{15}P = 0.5 \times \frac{8}{15}P = \frac{4}{15}P \)

Calculating the graduates among literate females:
- Graduates (females) = \( 40\% \) of \( \frac{7}{30}P = 0.4 \times \frac{7}{30}P = \frac{28}{300}P = \frac{14}{150}P = \frac{7}{75}P \)

### Step 4: Calculate the number of graduates in government jobs.
According to the problem:
- \( 20\% \) of graduate males are in government jobs.
- \( 28\frac{4}{7}\% \) of graduate females are in government jobs, which can be converted to \( \frac{28 \times 7 + 4}{7 \times 7} = \frac{200}{7}\% \).

Calculating the number of males in government jobs:
- Government jobs (males) = \( 20\% \) of \( \frac{4}{15}P = 0.2 \times \frac{4}{15}P = \frac{4}{75}P \)

Calculating the number of females in government jobs:
- Government jobs (females) = \( \frac{200}{7}\% \) of \( \frac{7}{75}P = \frac{200}{7000}P = \frac{2}{70}P = \frac{1}{35}P \)

### Step 5: Calculate the total number of people in government jobs.
Total in government jobs = Government jobs (males) + Government jobs (females)
- Total in government jobs = \( \frac{4}{75}P + \frac{1}{35}P \)

To add these fractions, we need a common denominator. The least common multiple of 75 and 35 is 525.

Converting each fraction:
- \( \frac{4}{75}P = \frac{4 \times 7}{75 \times 7}P = \frac{28}{525}P \)
- \( \frac{1}{35}P = \frac{1 \times 15}{35 \times 15}P = \frac{15}{525}P \)

Now, adding them:
- Total in government jobs = \( \frac{28}{525}P + \frac{15}{525}P = \frac{43}{525}P \)

### Step 6: Calculate the percentage of the total population in government jobs.
To find the percentage of the total population that is in government jobs:
- Percentage = \( \left( \frac{\text{Total in government jobs}}{P} \right) \times 100 = \left( \frac{\frac{43}{525}P}{P} \right) \times 100 = \frac{43}{525} \times 100 \)

Calculating this gives:
- Percentage = \( \frac{4300}{525} \approx 8.19\% \)

### Final Answer:
The number of males and females in government service is approximately \( 8.19\% \) of the total population of the village.

---