Question 13

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:

Solution

Statement A:

x : y = 3 : 1

$$x^3-y^3=\left(3k\right)^3-k^3=26k^3$$

This implies value ofÂ $$x^3-y^3$$ cannot be determined from the given information.

Therefore, statement A is incorrect.

Statement B:Â

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 =Â $$\frac{24}{3}=8$$

z + x = 36 + 8 = 44

Therefore, statement B is correct.

Statement C:

It is given,Â 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.

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