Discussion

Explanation:

As per the information given in the question, since 50 kids were sampled from each of the village, number of kids in the villages in each of the regions is as below:

NE Region ⇒ 150 × 50 = 7500

W Region ⇒ 250 × 50 = 12500

E Region ⇒ 200 × 50 = 10000

Further, 55% of 30000 or 16500 kids studied in G, 37% of 30000 or 11100 studied in P and 8% of 30000 or 2400 did not go to school. This further implies that in G, mothers of 3000 kids completed their primary education and in P and O, mothers of 8400 and 600 kids completed their education.

Now we need to bifurcate mothers of all these children into those who had dropped out and those who completed their primary education for each of the 3 regions i.e., G, P and O.

Let us construct the table as shown below

​​​​​​​

Following condition (1) we know that in S, 60% of the surveyed kids are in G. So this would mean that in S in G we have 60% of 10000 or 6000 kids.

Now out of these 6000 kids, 5100 kids mothers dropped out of school before completing primary education.

This means that mothers of 900 kids in S in G completed their primary education.

Now following condition (3), as the number of kids in G in NE was the same as the number of kids in G in W, the number of kids in each of these 2 categories will be (16500 – 6000)/2 or 5250 kids.

This means that the number of kids in G in NE and W whose mothers had completed primary education is 5250-4200 or 1050.

Now in S, out of 10000 kids, mothers of 5700 kids had dropped out of school before completing primary education. So mothers of 10000 – 5700 or 4300 kids completed their primary education. Out of these 4300, 900 were in G in S.

Now as per condition (1), all kids whose mothers had completed primary education, were in school.

This means that all kids in S whose mothers had completed their primary education were either in G or P.

Out of 4300, 900 were in G. So the remaining 4300 – 900 or 3400 will be in P. So a total of 300 + 3400 or 3700 kids.

This further implies that S in as the mothers of all those kids in S who dropped out of school, none of them completed their education. Now as per condition (2), as in NE among the O kids, 50% had mothers who dropped out, it would imply that the remaining 50% have completed their education. So if 300 mothers had dropped, it would imply that 300 mothers have completed their education in NE in O.

As a total of 600 mothers in O have completed their education and 300 out of these are from NE and none from S, it would mean that 300 mothers of kids from W in O completed their education. So in all in O, the number of mothers who completed their education from NE, W and S are 600, 1500 and 300 respectively.

Now the total number of kids in W that are in P is 12500 – 1500 – 5250 = 5750 and in P in NE is 7500 – 600 – 5250 = 1650.

Out of these 5750 kids in W that are in P, 1900 kids mothers have dropped out of primary education, which means 5750 – 1900 = 3850 kids mothers have not completed their primary education.

Also out of 1650 kids who in NE who are in P, 1650 – 500 or 1150 kids’ mothers have not completed their primary education. Our table is now complete. Let us draw up the final table

​​​​​​​

 Looking at the table, we can see that out of 10000 kids in S, 3700 were studying in P.

So, the Required Percentage = 370010000 × 100 = 37%

Hence, option (a).

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