If x is jointly proportional to the cube of y and the fourth power of z. In what ratio is x increased or decreased when y is halved and z is doubled?

A.
4:1 increase 
B.
2:1 increase 
C.
1:1 no change 
D.
1:4 decrease 
E.
3:4 decrease
Correct Answer: Option B
Explanation
(x propto y^{3} z^{4})
(x = ky^{3} z^{4})
If y is halved and z is doubled, we have
(x = k (frac{1}{2} y)^{3} (2z)^{4})
(x = k (frac{y^{3}}{8}) (16z^{4})))
(x = 2k y^{3} z^{4})
(therefore text{x is increased in the ratio 2 : 1})