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In 2017, the population of village C remained unchanged from 2015, but the number of literates increased by *X*. As a result, the total number of literates became 70\% more than the number of illiterates. What is the value of *X*?

Question

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In 2017, the population of village C remained unchanged from 2015, but the number of literates increased by *X*. As a result, the total number of literates became 70\% more than the number of illiterates. What is the value of *X*?

Accepted Answer

**Solution:**

1. Given that the total population of village C in 2015 is 10\% of 18000:
   - Population in 2015 = $18000 	imes \frac{10}{100} = 1800$

2. The population remains the same in 2017, so:
   - Population in 2017 = 1800

3. In 2015, illiterates are 40\% of village C's population:
   - Illiterates = $1800 	imes \frac{40}{100} = 720$

4. Literates in 2015 = Total population - Illiterates:
   - Literates = $1800 - 720 = 1080$

5. In 2017, literates increase by *X*, so:
   - Literates in 2017 = $1080 + X$
   - Illiterates in 2017 = $1800 - (1080 + X) = 720 - X$

6. According to the problem, literates are 70\% more than illiterates in 2017:
   $$1080 + X = (720 - X) 	imes \left(1 + \frac{70}{100}ight) = (720 - X) 	imes 1.7$$

7. Expanding and simplifying:
   $$1080 + X = 1224 - 1.7X$$
   $$X + 1.7X = 1224 - 1080$$
   $$2.7X = 144$$
   $$X = \frac{144}{2.7} = 53.33$$

**Note:** The original data in the question states illiterates as 1152 and literates as 648, which suggests a different percentage split. Recalculating with original values:

- Illiterates in 2015 = $18000 	imes \frac{40}{100} = 7200$ (this is total illiterates in all villages, not just village C)

- Village C population = $18000 	imes \frac{10}{100} = 1800$

- Illiterates in village C = $1800 	imes \frac{64}{100} = 1152$ (from original data)

- Literates in village C = $1800 - 1152 = 648$

Using these values:

$$648 + X = (1152 - X) 	imes 1.7$$

$$648 + X = 1958.4 - 1.7X$$

$$X + 1.7X = 1958.4 - 648$$

$$2.7X = 1310.4$$

$$X = \frac{1310.4}{2.7} = 485$$

**Answer:** $485$

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