Analyzing Workforce Distribution Data

The question asks for the ratio of the number of female workforce in the Construction and Maintenance (CM) sector to the number of male workforce in the Professional (PR) and Others (OT) sectors combined. We are given the total workforce, the percentage distribution across sectors, and the male to female ratio within each sector.

Understanding the Given Data

Total workforce in India across all sectors = 80 lakhs.

The table provides the percentage of this total workforce in each sector and the ratio of male to female workers within that sector.

Calculating Workforce in Specific Sectors

First, we need to calculate the total number of workers in the relevant sectors (CM, PR, and OT) based on their percentage distribution from the total workforce of 80 lakhs.

• Workforce in CM sector = $9\%$ of 80 lakhs = $\frac{9}{100} \times 80 \text{ lakhs} = 0.09 \times 80 \text{ lakhs} = 7.2 \text{ lakhs}$
• Workforce in PR sector = $18\%$ of 80 lakhs = $\frac{18}{100} \times 80 \text{ lakhs} = 0.18 \times 80 \text{ lakhs} = 14.4 \text{ lakhs}$
• Workforce in OT sector = $6\%$ of 80 lakhs = $\frac{6}{100} \times 80 \text{ lakhs} = 0.06 \times 80 \text{ lakhs} = 4.8 \text{ lakhs}$

Calculating Female Workforce in CM Sector

In the CM sector, the ratio of Male to Female workforce is 5 : 4. The total ratio parts are $5 + 4 = 9$. The total workforce in the CM sector is 7.2 lakhs.

The fraction of female workforce in CM is $\frac{4}{9}$.

Number of female workforce in CM = $\frac{4}{9} \times 7.2 \text{ lakhs} = 4 \times \frac{7.2}{9} \text{ lakhs} = 4 \times 0.8 \text{ lakhs} = 3.2 \text{ lakhs}$.

Calculating Male Workforce in PR Sector

In the PR sector, the ratio of Male to Female workforce is 5 : 7. The total ratio parts are $5 + 7 = 12$. The total workforce in the PR sector is 14.4 lakhs.

The fraction of male workforce in PR is $\frac{5}{12}$.

Number of male workforce in PR = $\frac{5}{12} \times 14.4 \text{ lakhs} = 5 \times \frac{14.4}{12} \text{ lakhs} = 5 \times 1.2 \text{ lakhs} = 6 \text{ lakhs}$.

Calculating Male Workforce in OT Sector

In the OT sector, the ratio of Male to Female workforce is 3 : 5. The total ratio parts are $3 + 5 = 8$. The total workforce in the OT sector is 4.8 lakhs.

The fraction of male workforce in OT is $\frac{3}{8}$.

Number of male workforce in OT = $\frac{3}{8} \times 4.8 \text{ lakhs} = 3 \times \frac{4.8}{8} \text{ lakhs} = 3 \times 0.6 \text{ lakhs} = 1.8 \text{ lakhs}$.

Calculating Total Male Workforce in PR and OT Sectors Put Together

Total male workforce in PR and OT sectors combined = Number of male workforce in PR + Number of male workforce in OT

Total male workforce (PR + OT) = $6 \text{ lakhs} + 1.8 \text{ lakhs} = 7.8 \text{ lakhs}$.

Calculating the Required Ratio

The question asks for the ratio of the number of female workforce in CM sector to the number of male workforce in PR and OT sectors put together.

Ratio = (Female workforce in CM) : (Male workforce in PR + OT)

Ratio = $3.2 \text{ lakhs} : 7.8 \text{ lakhs}$

To simplify the ratio, we can write it as a fraction and remove the decimals by multiplying both numbers by 10:

Ratio = $\frac{3.2}{7.8} = \frac{3.2 \times 10}{7.8 \times 10} = \frac{32}{78}$

Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

$\frac{32}{78} = \frac{32 \div 2}{78 \div 2} = \frac{16}{39}$

The ratio is 16 : 39.

Conclusion

Based on the data analysis and calculations, the ratio of the number of female workforce in the CM sector compared to the number of male workforce in the PR and OT sectors put together is 16 : 39.

Revision Table: Workforce Data Analysis

Reviewing the key values calculated:

Female workforce in CM = 3.2 lakhs

Male workforce in PR + OT = 6 lakhs + 1.8 lakhs = 7.8 lakhs

Ratio = 3.2 : 7.8 = 16 : 39

Additional Information: Data Interpretation Basics

Data interpretation questions often involve analyzing tables or charts to extract information and perform calculations. Key skills needed include:

• Percentage Calculations: Understanding how to find a percentage of a total value. If $X$ is $P\%$ of $Y$, then $X = \frac{P}{100} \times Y$.
• Ratio and Proportion: Understanding ratios like M:F means that for every M parts male, there are F parts female. The total number of parts is M+F. The fraction of males is $\frac{M}{M+F}$ and the fraction of females is $\frac{F}{M+F}$. These fractions are then applied to the total workforce in that category to find the actual numbers.
• Combining Data: Adding or subtracting values from different categories as required by the question (e.g., combining male workforce from two sectors).
• Ratio Simplification: Expressing ratios in their simplest form by dividing both numbers by their greatest common divisor.

Practicing these basic mathematical concepts is crucial for solving data interpretation problems accurately and efficiently.