Question

The third proportional $\frac{x^{2.5}}{y^{1.5}}\times z^{3.5}$ and ${x^{0.25}}\times \frac{y^{0.25}}{z^{-0.25}}$ is __________

• A. $$\frac{y^3}{x^3z^3}$$
• B. $$\frac{y^2}{x^2z^3}$$
• C. $$\frac{y^2}{x^2z^2}$$
• D. $$\frac{y^2}{x^3z^2}$$

Answer 1

Answer:

$$\frac{y^2}{x^2z^3}$$

The third proportional (c) of two quantities (a) and (b) satisfies:

$a : b = b : c \Rightarrow c = \frac{b^2}{a}$

Here,
$a = \frac{x^{2.5}}{y^{1.5}} \cdot z^{3.5}, \quad$
$b = x^{0.25} \cdot \frac{y^{0.25}}{z^{-0.25}}$

First simplify (b):
$b = x^{0.25} \cdot y^{0.25} \cdot z^{0.25}$

Now,
$b^2 = x^{0.5} \cdot y^{0.5} \cdot z^{0.5}$
Now compute:
$c = \frac{b^2}{a}$
$= \frac{x^{0.5} y^{0.5} z^{0.5}}{x^{2.5} y^{-1.5} z^{3.5}}$
Subtract powers:

• $For (x): (0.5 - 2.5 = -2)$

• $For (y): (0.5 - (-1.5) = 2)$

• $For (z): (0.5 - 3.5 = -3)$

So,
$c = x^{-2} \cdot y^2 \cdot z^{-3}$
$= \frac{y^2}{x^2 z^3}$