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
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(x \propto y^{3} z^{4}\)
\(x = ky^{3} z^{4}\)
If y is halved and z is doubled, we have
\(x = k (\frac{1}{2} y)^{3} (2z)^{4}\)
\(x = k (\frac{y^{3}}{8}) (16z^{4})\)\)
\(x = 2k y^{3} z^{4}\)
\(\therefore \text{x is increased in the ratio 2 : 1}\)
Source: Myschool Past Questions Archive (Record #32447)