**Core Concept**
The literacy rate is a measure of the percentage of people in a population who can read and write, typically calculated by dividing the number of literate individuals by the total population and multiplying by 100.

**Why the Correct Answer is Right**
To calculate the literacy rate, we need to divide the number of literate individuals (4000) by the total population (10,000) and then multiply by 100. The formula for literacy rate is (Number of literate individuals / Total population) x 100. In this case, (4000 / 10,000) x 100 = 40%. However, the question asks for the literacy rate of the population excluding children (0-6 years old), which is 10,000 - 2000 = 8000. Therefore, the literacy rate of the population excluding children is (4000 / 8000) x 100 = 50%.

**Why Each Wrong Option is Incorrect**
**Option A:** 30% - This option is incorrect because it underestimates the literacy rate of the population excluding children.
**Option B:** 40% - This option is incorrect because it does not take into account the exclusion of children from the population.
**Option D:** 60% - This option is incorrect because it overestimates the literacy rate of the population excluding children.

**Clinical Pearl / High-Yield Fact**
When calculating literacy rates, it's essential to consider the age group being studied, as children are often not considered literate in the same way as adults.

**✓ Correct Answer: C. 50%.**