Given, 3x + 4y = 20

Finding Quartile Deviation of x

- To find the quartile deviation of x, we first need to find the median of x.
- Median of x can be found by solving the equation 3x + 4y = 20 for x.
- 3x = 20 - 4y
- x = (20 - 4y)/3
- Median of x is the value of x when y = 0 (since y is not related to the median of x).
- So, x = (20 - 4*0)/3 = 20/3
- Now, we need to find the values of x corresponding to the first quartile (Q1) and third quartile (Q3).
- Q1 is the value of x for which 25% of the data lies below it, and Q3 is the value of x for which 75% of the data lies below it.
- To find Q1 and Q3, we need to solve the equation 3x + 4y = 20 for x when y takes values corresponding to the first quartile (Q1) and third quartile (Q3).
- Let Q1 = k and Q3 = m. Then, we have:
* 3k + 4y = 20 for the first quartile (Q1)
* 3m + 4y = 20 for the third quartile (Q3)
- Solving for y in both equations, we get:
* y = (20 - 3k)/4 for Q1
* y = (20 - 3m)/4 for Q3
- Substituting these values of y in the original equation, we get:
* 3k + 4[(20-3k)/4] = 20 for Q1
* 3m + 4[(20-3m)/4] = 20 for Q3
- Simplifying these equations, we get:
* k = 5 for Q1
* m = 35/3 for Q3
- Quartile deviation of x is given by (Q3 - Q1)/2.
- So, quartile deviation of x = (35/3 - 5)/2 = 5/3 * 2 = 10/3

Finding Quartile Deviation of y

- To find the quartile deviation of y, we need to use the formula:
* Quartile deviation of y = (quartile deviation of x) * (coefficient of y in the equation)/(coefficient of x in the equation)
- Coefficient of y in the equation 3x + 4y = 20 is 4, and coefficient of x is 3.
- So, quartile deviation of y = (10/3) * (4/3) = 40/9 = 4.44 (approx)
- Therefore, option D (9) is not the correct answer. The correct answer is option B (14) which is not given in the options.