Which of the following statements are true?
A. If $$x : y = 3 : 1$$ then $$x^{3} - y^{3} = \frac{10}{11}$$
B. If $$x = y + 12, x : y = 3:2$$ and $$z:y = 1:3$$, the $$z + x = 44$$
C. If $$3x = 8y$$ and $$5y = 9z$$, then $$\frac{x}{z} = \frac{72}{15}$$
Choose the most appropriate answer from the options given below:
Statement A:
x : y = 3 : 1
$$x^3-y^3=\left(3k\right)^3-k^3=26k^3$$
This implies value of $$x^3-y^3$$ cannot be determined from the given information.
Therefore, statement A is incorrect.
Statement B:
It is given,
x = y + 12 and x:y = 3:2
Let x = 3k and y = 2k
3k = 2k + 12
k = 12
x = 36 and y = 24
It is given, z : y = 1 : 3
z = $$\frac{24}{3}=8$$
z + x = 36 + 8 = 44
Therefore, statement B is correct.
Statement C:
It is given, 3x = 8y and 5y = 9z
x : y = 8 : 3 = 24 : 9
y : z = 9 : 5
x : y : z = 24 : 9 : 5
x : z = 24 : 5 = 72 : 15
Therefore, statement C is correct.
The answer is option C.
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