Statement A: x:y=3:1 x3−y3=(3k)3−k3=26k3 This implies value of x3−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.