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

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

$$\begin{array}{ccccc}  & \text{G} & \text{P} & \text{O} & \text{Total } \\ \text{NE} & 4200 & 500 & 300 & 5000 \\ \text{W} & 4200 & 1900  & 1200 & 7300 \\ \text{S} & 5100& 300 & 300 & 5700 \\ \text{Total} & 13500 & 2700 & 1800 & 18000 \end{array}$$

It is also known that:

  1. In $\text{S}$, $60\%$ of the surveyed kids were in $\text{G}$. Moreover, in $\text{S}$, all surveyed kids whose mothers had completed primary education were in school.
  2.  In $\text{NE}$, among the $\text{O}$ kids, $50\%$ had mothers who had dropped out before completing primary education
  3. The number of kids in $\text{G}$ in $\text{NE}$ was the same as the number of kids in $\text{G}$ in $\text{W}$.

In a follow up survey of the same kids two years later, it was found that all the kids were now in school. Of the kids who were not in school earlier, In one region, $25\%$ were in $\text{G}$ now, whereas the rest were enrolled in $\text{P}$; in the second region, all such kids were in $\text{G}$ now; while the third region, $50\%$ of such kids had now joined while the rest had joined $\text{P}$. As a result in all three regions put together, $50\%$ of the kids who were earlier out of school had joined $\text{G}$. It was also seen that no surveyed kid had changed schools.

What number of the surveyed kids now were in $\text{G}$ in $\text{W}$?

  1. $6000$
  2. $5250$
  3. $6750$
  4. $6300$
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