Directions: The following table gives the percentage distribution of population of five states, P, Q, R, S and T on the basis of poverty line and also on the basis of sex. Study the table and answer the questions based on it. | State | Percentage of Population below Poverty line | Proportion of Males and Females Below Poverty line M : F | Proportion of Males and Females Above Poverty Line M : F | |---|---|---|---| | P | 35 | 5 : 6 | 6 : 7 | | Q | 25 | 3 : 5 | 4 : 5 | | R | 24 | 1 : 2 | 2 : 3 | | S | 19 | 3 : 2 | 4 : 3 | | T | 15 | 5 : 3 | 3 : 2 | If the male population above poverty line for State R is 1.9 million, then the total population of State R is :

### Concept & Reverse Calculation We reverse-engineer the total population by equating the given sub-segment value to its algebraic representation using the known percentages and ratios. $$ \text{Total Pop} \times \% \text{ Above Poverty} \times \text{Male Fraction} = \text{Given Male Population} $$ ### Step-by-Step Solution 1. **Define Total Population:** Let the total population of State R be $x$. 2. **Find fraction above poverty line:** Since $24\%$ are below the poverty line, $100\% - 24\% = 76\%$ are above the poverty line. So, population above = $0.76x$. 3. **Determine male fraction above poverty:** The M : F ratio above the poverty line in State R is $2 : 3$. Thus, the male fraction is $\frac{2}{5}$. 4. **Set up the equation:** $$ 0.76x \times \left(\frac{2}{5}\right) = 1.9 $$ $$ 0.76x \times 0.4 = 1.9 $$ $$ 0.304x = 1.9 $$ 5. **Solve for $x$:** $x = \frac{1.9}{0.304} = \frac{1900}{304} = 6.25$ million. ### Exam Strategy & Shortcut Work with fractions to simplify division: $x \times \left(\frac{76}{100}\right) \times \left(\frac{2}{5}\right) = 1.9$. Rearrange as $x = \frac{1.9 \times 500}{152} = \frac{950}{152}$. Divide numerator and denominator by 2 to get $\frac{475}{76} = 6.25$. ### Common Pitfall Using the wrong fraction from the ratio ($2/3$ instead of $2/5$). Remember the denominator must be the sum of the ratio components ($2+3=5$). ### Final Answer Therefore, the correct answer is **6.25 million**.