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 (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 arid 200 villages from S. It was found that of the 30000 surveyed feds 55% studied in primary schools run by government (G), 37% in private schools (P) white 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:
| 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:
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 G now, whereas the rest were enrolled in P; in the second region, all such kids were in G now; while in the third region, 50% of such kids had now joined G while the rest had joined P. As a result, in all three regions put together, 50% of the kids who were earlier out of school had joined G. It was also seen that no surveyed kid had changed schools.
What number of the surveyed kids now were in G in W?
Correct Answer :
6000
Solution :
The correct option is A.
First, let's determine the original number of government school (G) kids in region W:
Total G kids overall = 55% of 30,000 = 16,500.
In S, 60% of kids were in G. So, total G in S = 60% of 10,000 = 6,000.
Since the number of kids in G in NE was the same as the number of kids in G in W, let this be x.
So, x + x + 6,000 = 16,500 ⇒ 2x = 10,500 ⇒ x = 5,250.
Thus, originally G in W was 5,250.
Next, let's look at the out-of-school (O) kids in each region:
Total O in NE = 600 (300 dropped out + 300 completed)
Total O in W = 1,500 (1,200 dropped out + 300 completed)
Total O in S = 300 (300 dropped out + 0 completed)
Total O = 2,400.
Two years later, 50% of the O kids (1,200 kids) joined G. The three strategies used by the regions are:
- Strategy 1: 25% join G
- Strategy 2: 100% join G
- Strategy 3: 50% join G
Let's map the regions to the strategies to get a sum of 1,200:
If W (1,500) has Strategy 3 (50%), then G-enrolment from W = 750.
Remaining to make 1,200 is 450. This is achieved if NE (600) has Strategy 1 (25% of 600 = 150) and S (300) has Strategy 2 (100% of 300 = 300).
Since 750 + 150 + 300 = 1,200, this is the unique valid distribution.
Therefore, the new number of kids in G in W is:
Original G in W + O kids in W who joined G = 5,250 + 750 = 6,000.
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