Explanation:

Sure, let's break down the problem:

- The relation given is 9p = 3q = 2r = 6s. Let's find a common representation for these angles.

- Suppose x is the common value such that:

9p = x => p = x/9

3q = x => q = x/3

2r = x => r = x/2

6s = x => s = x/6

- Since the entire circle of a pie chart is 360 degrees, we have:

p + q + r + s = 360 degrees.

- Substituting the values of p, q, r, and s, we get:

(x/9) + (x/3) + (x/2) + (x/6) = 360.

- Solving, we have a common denominator of 18:

(2x/18) + (6x/18) + (9x/18) + (3x/18) = 360

=> (20x/18) = 360

=> x = 324.

- Using x = 324, find:

p = 324/9 = 36

q = 324/3 = 108

r = 324/2 = 162

s = 324/6 = 54.

- Now, find 4p - q:

4p = 4 * 36 = 144

4p - q = 144 - 108 = 36.

- Thus, the correct answer is Option 4: 36.

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