Explanation:

Based on the information given:

- Let the population of village B be \( x \).

- Therefore, the population of village A is 35% less, which is \( x - 0.35x = 0.65x \).

- Total population: \( x + 0.65x = 8250 \). Solving gives \( x = 5000 \).

- So, the population of village B is 5000 and village A is 3250.

- The adult-to-children ratio across both villages is 20:13.

- Therefore, adults and children together = 20k + 13k = 33k; given the difference = 1750.

- Solving gives \( 20k - 13k = 1750 \) leading to \( k = 250 \).

- Total adults across both villages = \( 20 \times 250 = 5000 \).

Thus, the average adult population is \( 5000/2 = 2500 \).

- Analyzing all relevant options, we see that Option 3: 2500 is correct.