In the county of Veenapaniville, there are a total of 50

can double matrix be employed here to solve the problem
though i have seen it save time on problems i a not sure where exactly doed it work

please suggest me if its possible

You can certainly use double matrix in this question though I doubt its time saving ability in this question.
Make something like this:

......................A...........B...........C.........Total
Public
Parochial
Private
............................................................50

Now put the numbers in.

That said, the question is quite straight forward. All you need to do is focus on what you need. You need to find the number of private schools in A. Total no. of private schools is 9 and in B, you have 2 of them. So there are 7 private schools distributed between A and C. All you need to find is the number of private schools in C to get the number of private schools in A. What is given to you about C? C has an equal number of each of the three kinds of schools. Total number of schools in C = 50 - (18 + 17) = 15. So no. of private schools in C = 15/3 = 5
Therefore, A must have 7 - 5 = 2 private schools.

Solution Attached !!!

A( 18) B(15+2) C (15= 5+5+5)

9-7 = 2 independent high school in A

While the double matrix method does provide a more structured answer to ensure you don't miss out on important information. With practice you will realize you don't need all that data if you focus on what the stem is specifically asking for.

In this Q, we need to find the "how many private independent schools are there in District A". So isolate all the data related to that type of school.

We get the following statements on doing that:-

1) There are 9 private independent schools
2) District B has 17 high schools total, and only two of those are private independent schools
3) District C has an equal number of each of the three kinds of schools i.e of the total of 15 schools in District C, 5 are private independent schools

Thus the no of private independent schools in District A= Total no of private independent schools- private independent schools in B and C
= 9- 2-5 = 2

Hope that helps!

Total: 50

Let public(a); parochial(b) and private(c)

District A: \(a_A + b_A + c_A = 18\)

District B: \(a_B + b_B + c_B = 17\)

District C: \(a_C + b_C + c_C = 15 [ 50 - 18 - 17]\)

=> If District C has an equal number of each of the three kinds of schools \(a_C = b_C = c_C \)

Therefore, \(a_C = b_C = c_C = 5\)

District B has 17 high schools total, and only two of those are private independent schools: \(c_B = 2\)

Total c: \(c_A + c_B + c_C = 9 \)

=> \(c_A = 9 - 2 - 5 = 2\)

Answer A

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