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 30,000 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:

North East (NE)

West (W)

South (S)

Overall Totals

Question 1

What percentage of kids from S were studying in P?

A. 37%
B. 6%
C. 79%
D. 56%

Question 2

Among the kids in W whose mothers had completed primary education, how many were not in school?

A. 300
B. 1200
C. 1050
D. 1500

Question 3

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?

A. 6000
B. 5250
C. 6750
D. 6300

Question 4

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 percentage of the surveyed kids in S, whose mothers had dropped out before completing primary education, were in G now?

A. 94.7%
B. 89.5%
C. 93.4%
D. Cannot be determined from the given information.

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Set 1

Given Base Data

Total kids surveyed:
NE = 150 × 50 = 7,500
W = 250 × 50 = 12,500
S = 200 × 50 = 10,000
Total = 30,000

Overall:
G = 55% of 30,000 = 16,500
P = 37% of 30,000 = 11,100
O = 8% of 30,000 = 2,400

Step 1: Complete the Region-wise Total Table

For S, 60% were in G.
So, S in G = 60% of 10,000 = 6,000

From dropout table, S in G = 5,100.
So, S completed-mother kids in G = 6,000 − 5,100 = 900

Also, in S, all kids whose mothers completed primary education were in school.
So, completed-mother kids in O = 0

Total completed-mother kids in S = 10,000 − 5,700 = 4,300
So, completed-mother kids in P = 4,300 − 900 = 3,400

Therefore, total S in P = 300 + 3,400 = 3,700

Q1. What percentage of kids from S were studying in P?

S in P = 3,700
Total S kids = 10,000

Percentage = 3,700 / 10,000 × 100 = 37%

Answer 1: A. 37%

Q2 Answer: A. 300

Step 2: Find W completed-mother kids not in school

In NE, among O kids, 50% had mothers who dropped out.
Dropout NE O = 300
So, total NE O = 600

Total NE kids = 7,500

Given NE G = W G.
Overall G = 16,500
S G = 6,000

So, NE G + W G = 16,500 − 6,000 = 10,500
Since NE G = W G, each = 5,250

Now find P totals:

NE P = 7,500 − 5,250 − 600 = 1,650

Overall P = 11,100
S P = 3,700
NE P = 1,650

So, W P = 11,100 − 3,700 − 1,650 = 5,750

W total = 12,500
W G = 5,250
W P = 5,750

So, W O = 12,500 − 5,250 − 5,750 = 1,500

From dropout table, W dropout O = 1,200

So, W completed-mother O = 1,500 − 1,200 = 300

Q3 Answer: A. 6000

Step 3: Follow-up survey

Earlier out-of-school kids:

NE O = 600
W O = 1,500
S O = 300
Total O = 2,400

Now, 50% of earlier O kids joined G.
So, total joined G = 50% of 2,400 = 1,200

The three region percentages are 25%, 100%, and 50%.

Check assignment:

NE = 25% of 600 = 150
W = 50% of 1,500 = 750
S = 100% of 300 = 300

Total = 150 + 750 + 300 = 1,200

So, W earlier O kids joining G = 750

Original W G = 5,250
Now W G = 5,250 + 750 = 6,000

Q4 Answer: A. 94.7%

Percentage of surveyed kids in S whose mothers had dropped out before completing primary education, who were in G now

From dropout table for S:

S dropout total = 5,700
S dropout G originally = 5,100
S dropout O originally = 300

In S, all earlier O kids joined G.
So, S dropout kids now in G = 5,100 + 300 = 5,400

Percentage = 5,400 / 5,700 × 100 = 94.7%