Question

If z varies directly as x and inversely as y. Find the percentage increase in z due to an increase of 12% in x and a decrease of 20% in y.

Answer 1

z=kx/y
where k is a constant
percentage increase in z =percentage increase in x-percentage decrease in y
=+12-(-20)
=12+20
=32

Answer 2

Answer: There is increase of 40% in z.

Step-by-step explanation:

Since we have given that

z varies directly as x and inversely as y.

$z_1=\frac{kx}{y}--------------(1)$

since there is an increase of 12% in x and a decrease of 20% in y.

so, it becomes,

$z_2=\frac{k1.12x}{0.8y}-------------(2)$

Dividing Eq(1) by Eq(2) , we get,

$\frac{z_1}{z_2}=\frac{\frac{kx}{y}}{\frac{1.12xk}{0.8y}}\\\\z_1=\frac{80}{112}z_2$

We need to find the change in z:

$\frac{z_2-z_1}{z_1}\times 100\\\\=\frac{(1-\frac{80}{112})z_1}{\frac{80}{112}}\times 100\\\\=\frac{32}{80}\times 100\\\\=40\%$

Hence, there is 40% of increase in z.