Q1. Which of the following statements is true?
A. If x:y= 3:1 then x3 – y3 = 10 / 11
B. If x = y + 12, x:y = 3:2 and z:y = 1:3, then z+x = 44
C. If 3x= 8y and 5y = 9z, then x/z= 72 / 15
Choose the most appropriate answer from the options given below:
A. A and B only
B. A and C only
C. B and C only
D. A, B, and C
EXPLANATION
Answer: C
Statement A:
x : y = 3 : 1
x3 − y3 = (3k)3 − k3 = 26k3
This implies value of x3
z – y3 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= 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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