Explanation:

Let's break down the information step by step:

- Let the population of village B be x. Then, A = x - 35% of x = 0.65x.

- Total population: A + B = 0.65x + x = 1.65x = 8250.

? x = 8250 / 1.65 = 5000. ? B = 5000, A = 3250.

- Adults : Children = 20 : 13 (Total population 8250)

- So, Adults = (20/33)*8250 = 5000, Children = (13/33)*8250 = 3250.

- Difference between adults and children = 1750 (Given, matches 5000 – 3250).

- In village A: Adults = 60% more than children.

- Let children in A = y, adults = y + 0.6y = 1.6y; so y + 1.6y = 2.6y = 3250 ? y = 1250 (children), adults = 2000.

- In village B: Let children = z, adults = 1.5z; z + 1.5z = 2.5z = 5000 ? z = 2000 (children), adults = 3000.

- Ratio of children in A to B = 1250 : 2000 = 5 : 8.

Thus, the correct option is:

- Option 2: 5 : 8

Explanation of Options:

- 3 : 5, 5 : 3, 4 : 7, 7 : 8 are all not matching calculated ratio (5 : 8).

- Only option 2 (5 : 8) is correct and matches the calculation.