In a country 55% of the population is women. 80% of the male population is literate. If the total literacy rate is 58% then what percentage of women are literate?

Steps to Solve

1. Define Variables Let the total population be $P$.

2. Calculate Male and Female Population

• Women population = $0.55P$
• Male population = $0.45P$

3. Determine Literate Males Given 80% of males are literate: Literate males = $0.8 \times 0.45P = 0.36P$

4. Calculate Total Literate Population The total literacy rate is 58%: Total literate population = $0.58P$

5. Set Up the Equation Let $x$ be the percentage of literate women. Then the equation is: $$0.36P + \frac{x}{100} \times 0.55P = 0.58P$$

6. Solve for $x$ Rearranging the equation, we have: $$ \frac{x}{100} \times 0.55P = 0.58P - 0.36P $$

This simplifies to: $$ \frac{x}{100} \times 0.55P = 0.22P $$

Dividing both sides by $0.55P$ gives: $$ \frac{x}{100} = \frac{0.22}{0.55} $$

Finally, multiply by 100 to find $x$: $$ x = \left(\frac{0.22}{0.55}\right) \times 100 $$

7. Calculate $x$ Calculating the above expression: $$ x = 40 $$