The table below shows data about five villages (A, B, C, D & E) including the percentage of literate population, literate males, percentage of male illiterate population out of total illiterate, and total females (literate + illiterate). Using the data for village E, find the total population of village E.

| Villages | % of literate population | Male literate | Male illiterate (in %) out of total illiterate | Total female (Literate + Illiterate) |
|----------|--------------------------|---------------|-----------------------------------------------|-------------------------------------|
| E | 85 | 1530 | 60% | 1746 |

Question

The table below shows data about five villages (A, B, C, D & E) including the percentage of literate population, literate males, percentage of male illiterate population out of total illiterate, and total females (literate + illiterate). Using the data for village E, find the total population of village E.

| Villages | % of literate population | Male literate | Male illiterate (in %) out of total illiterate | Total female (Literate + Illiterate) |
|----------|--------------------------|---------------|-----------------------------------------------|-------------------------------------|
| E        | 85                       | 1530          | 60%                                          | 1746                                |

Accepted Answer

**Solution:**

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

2. The literate population is $85\%$ of total population, so:
   $$	ext{Literate population} = 85x$$

3. The illiterate population is the remainder:
   $$	ext{Illiterate population} = 100x - 85x = 15x$$

4. Given literate male population = 1530, so literate female population is:
   $$85x - 1530$$

5. Male illiterate population is $60\%$ of total illiterate population:
   $$	ext{Male illiterate} = 15x 	imes \frac{60}{100} = 9x$$

6. Female illiterate population:
   $$15x - 9x = 6x$$

7. Total female population (literate + illiterate) is given as 1746, so:
   $$6x + (85x - 1530) = 1746$$

8. Simplify the equation:
   $$6x + 85x - 1530 = 1746$$
   $$91x = 1746 + 1530 = 3276$$

9. Solve for $x$:
   $$x = \frac{3276}{91} = 36$$

10. Therefore, total population of village E:
    $$100x = 100 	imes 36 = 3600$$

**Answer:** $3600$

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