If `1/5 :1/x = 1/x : 1/(1.25)` then the value of x is

Options

A. `1.5`
B. `2`
C. `2.5`
D. 3.5

Answer

To solve the problem \( \frac{1}{5} : \frac{1}{x} = \frac{1}{x} : \frac{1}{1.25} \), we will follow these steps:

### Step 1: Set up the ratio
We start with the given ratio:
\[ \frac{1}{5} : \frac{1}{x} = \frac{1}{x} : \frac{1}{1.25} \]

### Step 2: Rewrite the ratios
Using the property of ratios, we can rewrite the first ratio as:
\[ \frac{1}{5} : \frac{1}{x} \implies x : 5 \]
And the second ratio as:
\[ \frac{1}{x} : \frac{1}{1.25} \implies 1.25 : x \]

So we can rewrite the equation as:
\[ x : 5 = 1.25 : x \]

### Step 3: Cross-multiply
Cross-multiplying gives us:
\[ x^2 = 5 \cdot 1.25 \]

### Step 4: Calculate the right-hand side
Now, we calculate \( 5 \cdot 1.25 \):
\[ 5 \cdot 1.25 = 6.25 \]
Thus, we have:
\[ x^2 = 6.25 \]

### Step 5: Solve for \( x \)
Taking the square root of both sides:
\[ x = \sqrt{6.25} \]
Calculating the square root:
\[ x = 2.5 \]

### Final Answer
The value of \( x \) is \( 2.5 \).

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