In village D, the difference between the male and female population is 1152. Given the following data:

- Total population of village D = $100x$
- Percentage of literate population = 96\% of total population
- Among literates, 70\% are males and 30\% are females
- Among illiterates, 50\% are males and 50\% are females

Find the total number of illiterate females in village D.

Question

In village D, the difference between the male and female population is 1152. Given the following data:

- Total population of village D = $100x$
- Percentage of literate population = 96\% of total population
- Among literates, 70\% are males and 30\% are females
- Among illiterates, 50\% are males and 50\% are females

Find the total number of illiterate females in village D.

Accepted Answer

**Solution:**

1. Let the total population of village D be $100x$.

2. Total literate population = $96\%$ of $100x = 96x$.

3. Total illiterate population = $100x - 96x = 4x$.

4. Literate males = $70\%$ of literates = $96x 	imes \frac{70}{100} = 67.2x$.

5. Literate females = $30\%$ of literates = $96x 	imes \frac{30}{100} = 28.8x$.

6. Illiterate males = $50\%$ of illiterates = $4x 	imes \frac{50}{100} = 2x$.

7. Illiterate females = remaining illiterates = $4x - 2x = 2x$.

8. According to the problem, the difference between male and female population is 1152:

$$	ext{Male population} - 	ext{Female population} = 1152$$

Male population = Literate males + Illiterate males = $67.2x + 2x = 69.2x$

Female population = Literate females + Illiterate females = $28.8x + 2x = 30.8x$

So,
   $$69.2x - 30.8x = 1152$$
   $$38.4x = 1152$$
   $$x = \frac{1152}{38.4} = 30$$

9. Total illiterate females = $2x = 2 	imes 30 = 60$.

**Answer:** 60

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