A study to look at the early learning of rural kids was carried out in a number of villages spanning three states, chosen from the North East (NE), the West (W) and the South (S). 50 four-year old kids each were sampled from each of the 150 villages from NE, 250 villages from W and 200 villages from S. It was found that of the 30000 surveyed kids 55% studied in primary schools run by government (G), 37% in private schools (P) while the remaining 8% did not go to school (O).

The kids surveyed were further divided into two groups based on whether their mothers dropped out of school before completing primary education or not. The table below gives the number of kids in different types of schools for mothers who dropped out of school before completing primary education:

State	G	P	O	Total
NE	4200	500	300	5000
W	4200	1900	1200	7300
S	5100	300	300	5700
Total	13500	2700	1800	18000

It is also known that:

1. In S, 60% of the surveyed kids were in G. Moreover, in S, all surveyed kids whose mothers had completed primary education were in school.

2. In NE, among the O kids, 50% had mothers who had dropped out before completing primary education.

3. The number of kids in G in NE was the same as the number of kids in G in W.

What percentage of kids from S were studying in P?

The correct option is A.

Let's solve the problem systematically by analyzing the given information:

1. Calculate total kids surveyed in each state:
- NE: 150 villages × 50 kids/village = 7,500 kids
- W: 250 villages × 50 kids/village = 12,500 kids
- S: 200 villages × 50 kids/village = 10,000 kids
- Total kids = 7,500 + 12,500 + 10,000 = 30,000 kids.

2. Analyze State S (South):
- Total kids in S = 10,000.
- From condition 1: 60% of the surveyed kids in S were in G.

$\text{Kids in G in S}=60\%\times 10,000=6,000$

- The table shows that for mothers who dropped out, the number of kids in S under G is 5,100.
- Thus, the number of kids in G in S whose mothers completed primary education is:

$6,000-5,100=900$

3. Analyze the O (Out of school) category in S:
- From condition 1: In S, all surveyed kids whose mothers had completed primary education were in school (meaning none of them were in O).
- This implies that all kids in O in S must have mothers who dropped out of school.
- From the table, the number of kids in O in S for mothers who dropped out is 300.
- Therefore, the total number of kids in O in S is exactly 300.

4. Calculate kids in P in S:
- The total kids in S is 10,000.
- We know:
- Kids in G in S = 6,000
- Kids in O in S = 300
- Therefore, the total kids in P in S must be:

$\text{Total in P}=\text{Total kids}-(\text{G}+\text{O})=10,000-(6,000+300)=3,700$

Wait, let's check the percentage of kids from S studying in P:

$\text{Percentage}=\frac{3,700}{10,000}\times 100=37\%$

Wait! Let's re-verify the calculations. If 37% of kids from S were studying in P, then Option A is 37%. But wait, let's verify if the question asks for the percentage of kids whose mothers had completed primary education, or overall kids. The question asks: "What percentage of kids from S were studying in P?"
Let's check if the percentage is indeed 37% or 6%. If the question is "What percentage of kids from S were studying in P?", then it is 37% (Option A). Wait! Let's check the options: A) 37%, B) 6%, C) 79%, D) 56%. If the calculation gives 37%, then Option A is the correct option (Option A). Let's review if the index in the JSON should be 0 (for Option A) or if the correct option is B (6%). Let's check if there is an alternative interpretation where it is 6% (which is Option B, Option B).
Let's calculate the percentage of kids in P in S whose mothers completed education:
- Total kids in S with mothers who completed education = 10,000 - 5,700 = 4,300.
- Kids in P in S with mothers who completed education = 3,700 - 300 = 3,400.
Regardless, the correct option matching the question "What percentage of kids from S were studying in P?" is 37% (Option A, Option A).