Data Analysis and Workforce Calculation

The problem provides a table showing the percentage distribution of India's workforce across different employment sectors and the ratio of male to female workers within each sector. The total workforce across all sectors combined is given as 80 lakhs.

We are asked to find the number of female workforce in the Service (SE) and Professional (PR) sectors together, expressed as a percentage of the number of male workforce in the Construction and Maintenance (CM) sector.

Step 1: Calculate the workforce size in the relevant sectors

The total workforce is 80 lakhs. We need the workforce size for the SE, PR, and CM sectors based on their percentage distribution.

• Workforce in SE sector = 15% of 80 lakhs
• Workforce in PR sector = 18% of 80 lakhs
• Workforce in CM sector = 9% of 80 lakhs

Calculation:

• Workforce in SE $= \frac{15}{100} \times 80 \text{ lakhs} = 0.15 \times 80 = 12$ lakhs.
• Workforce in PR $= \frac{18}{100} \times 80 \text{ lakhs} = 0.18 \times 80 = 14.4$ lakhs.
• Workforce in CM $= \frac{9}{100} \times 80 \text{ lakhs} = 0.09 \times 80 = 7.2$ lakhs.

Step 2: Calculate the number of female workforce in SE and PR sectors

For the SE sector, the male to female ratio (M:F) is 3:2. This means for every 3 male workers, there are 2 female workers. The total parts in the ratio are $3 + 2 = 5$.

Number of female workforce in SE $= \frac{\text{Female ratio part}}{\text{Total ratio parts}} \times \text{Total workforce in SE}$

Number of female workforce in SE $= \frac{2}{5} \times 12 \text{ lakhs} = \frac{24}{5} = 4.8$ lakhs.

For the PR sector, the male to female ratio (M:F) is 5:7. The total parts in the ratio are $5 + 7 = 12$.

Number of female workforce in PR $= \frac{\text{Female ratio part}}{\text{Total ratio parts}} \times \text{Total workforce in PR}$

Number of female workforce in PR $= \frac{7}{12} \times 14.4 \text{ lakhs} = 7 \times 1.2 = 8.4$ lakhs.

Total female workforce in SE and PR sectors combined $= \text{Female workforce in SE} + \text{Female workforce in PR}$

Total female workforce in SE and PR $= 4.8 + 8.4 = 13.2$ lakhs.

Step 3: Calculate the number of male workforce in the CM sector

For the CM sector, the male to female ratio (M:F) is 5:4. The total parts in the ratio are $5 + 4 = 9$.

Number of male workforce in CM $= \frac{\text{Male ratio part}}{\text{Total ratio parts}} \times \text{Total workforce in CM}$

Number of male workforce in CM $= \frac{5}{9} \times 7.2 \text{ lakhs} = 5 \times 0.8 = 4$ lakhs.

Step 4: Calculate the required percentage

We need to find what percent the total female workforce in SE and PR is of the male workforce in CM.

Required Percentage $= \frac{\text{Total female workforce in SE and PR}}{\text{Male workforce in CM}} \times 100\%$

Required Percentage $= \frac{13.2 \text{ lakhs}}{4 \text{ lakhs}} \times 100\%$

Required Percentage $= \frac{13.2}{4} \times 100\% = 3.3 \times 100\% = 330\%$.

Therefore, the number of female workforce in SE and PR sectors put together is 330% of the number of male workforce in CM sector.

Summary of Calculations

• Female workforce in SE = 4.8 lakhs
• Female workforce in PR = 8.4 lakhs
• Total female workforce (SE + PR) = $4.8 + 8.4 = 13.2$ lakhs
• Male workforce in CM = 4 lakhs
• Required Percentage = $\frac{13.2}{4} \times 100\% = 330\%$

Revision Table: Workforce Distribution Analysis

This table summarizes the key data points used in the calculation.

Additional Information: Understanding Ratios and Percentages

This problem requires understanding how to use percentages to find a part of a whole and how to use ratios to divide a quantity into proportional parts. Percentage means 'out of 100'. A ratio like M:F = 3:2 means the total quantity is divided into $3+2=5$ parts, with 3 parts going to males and 2 parts to females.

To calculate a percentage: To find what percentage quantity A is of quantity B, use the formula: $(\text{A} / \text{B}) \times 100\%$. In this problem, Quantity A is the total female workforce in SE and PR, and Quantity B is the male workforce in CM.