Directions: In the following question, two quantities, labeled Quantity I and Quantity II, are given. You are required to determine the relationship between the two quantities and select the appropriate option. Compare only numerical values.

Given that a > b, a > 4, and b < 5.

$\text{Quantity I}\frac{1}{a}+\frac{1}{b}=0$

$\text{Quantity II}{(\frac{1}{b}-\frac{1}{a})}^2=0$

The correct option is Quantity I = Quantity II or no relation.

We are given the following conditions for the variables $a$ and $b$:

1. $a>b$

2. $a>4$

3. $b<5$

We need to compare the following two quantities:

$\text{Quantity I:}\frac{1}{a}+\frac{1}{b}$

$\text{Quantity II:}{(\frac{1}{b}-\frac{1}{a})}^2$

Let us test different valid values for $a$ and $b$ to determine if a consistent relationship exists.

Case 1: Assume positive values for both variables.

Let $a=5$ and $b=2$.

Checking the conditions: $5>2$, $5>4$, and $2<5$. All given conditions are satisfied.

Now, evaluate Quantity I:

$\text{Quantity I}=\frac{1}{5}+\frac{1}{2}=0.2+0.5=0.7$

Next, evaluate Quantity II:

$\text{Quantity II}={(\frac{1}{2}-\frac{1}{5})}^2={(0.5-0.2)}^2={\left(0.3\right)}^2=0.09$

In this case, Quantity I (0.7) > Quantity II (0.09).

Case 2: Assume a negative value for $b$.

Let $a=5$ and $b=-1$.

Checking the conditions: $5>-1$, $5>4$, and $-1<5$. All given conditions are satisfied.

Now, evaluate Quantity I:

$\text{Quantity I}=\frac{1}{5}+\frac{1}{-1}=0.2-1=-0.8$

Next, evaluate Quantity II:

$\text{Quantity II}={(\frac{1}{-1}-\frac{1}{5})}^2={(-1-0.2)}^2={(-1.2)}^2=1.44$

In this case, Quantity I (-0.8) < Quantity II (1.44).

Since Quantity I can be greater than Quantity II in some valid cases and less than Quantity II in other valid cases, no consistent relationship can be established between the two quantities.

Therefore, the relationship between Quantity I and Quantity II cannot be determined.