There are `(2)/(3)` men in a village and the rest are women. `80%` of the number of men and `70%` of number of women are literate. `40%` of literate men and `30%` of literate women are graduate. `20%` of graduate men and `25%` of graduate women have government jobs. Working population of that village is what percent of total population?

Answer

To solve the problem step by step, we will break down the calculations based on the information provided.

### Step 1: Determine the Total Population
Let's assume the total population of the village is 300.

### Step 2: Calculate the Number of Men and Women
- Men: \(\frac{2}{3}\) of the total population
\[ \text{Number of Men} = \frac{2}{3} \times 300 = 200 \]
- Women: The rest of the population
\[ \text{Number of Women} = 300 - 200 = 100 \]

### Step 3: Calculate the Number of Literate Men and Women
- Literate Men: \(80\%\) of the number of men
\[ \text{Literate Men} = 80\% \times 200 = 0.8 \times 200 = 160 \]
- Literate Women: \(70\%\) of the number of women
\[ \text{Literate Women} = 70\% \times 100 = 0.7 \times 100 = 70 \]

### Step 4: Calculate the Number of Graduate Men and Women
- Graduate Men: \(40\%\) of literate men
\[ \text{Graduate Men} = 40\% \times 160 = 0.4 \times 160 = 64 \]
- Graduate Women: \(30\%\) of literate women
\[ \text{Graduate Women} = 30\% \times 70 = 0.3 \times 70 = 21 \]

### Step 5: Calculate the Number of Men and Women with Government Jobs
- Government Jobs for Men: \(20\%\) of graduate men
\[ \text{Men with Government Jobs} = 20\% \times 64 = 0.2 \times 64 = 12.8 \]
- Government Jobs for Women: \(25\%\) of graduate women
\[ \text{Women with Government Jobs} = 25\% \times 21 = 0.25 \times 21 = 5.25 \]

### Step 6: Calculate the Total Working Population
\[ \text{Total Working Population} = \text{Men with Government Jobs} + \text{Women with Government Jobs} \]
\[ \text{Total Working Population} = 12.8 + 5.25 = 18.05 \]

### Step 7: Calculate the Percentage of Working Population
\[ \text{Percentage of Working Population} = \left(\frac{\text{Total Working Population}}{\text{Total Population}}\right) \times 100 \]
\[ \text{Percentage of Working Population} = \left(\frac{18.05}{300}\right) \times 100 \approx 6.01\% \]

### Final Answer
The working population of the village is approximately \(6.01\%\) of the total population.

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