If 3.4% of `600xx2.5%` of x = 382.5, then the value of x is :

Options

A. 800
B. 775
C. 825
D. 750

Answer

To solve the equation \(3.4\% \text{ of } 600 \times 2.5\% \text{ of } x = 382.5\), we will follow these steps:

### Step 1: Convert percentages to fractions
Convert \(3.4\%\) and \(2.5\%\) into fractions:
\[ 3.4\% = \frac{3.4}{100} = \frac{34}{1000} \]
\[ 2.5\% = \frac{2.5}{100} = \frac{25}{1000} \]

### Step 2: Substitute the fractions into the equation
Now substitute these fractions into the equation:
\[ \frac{34}{1000} \times 600 \times \frac{25}{1000} \times x = 382.5 \]

### Step 3: Simplify the left side
First, calculate \( \frac{34}{1000} \times 600 \):
\[ \frac{34 \times 600}{1000} = \frac{20400}{1000} = 20.4 \]
Now substitute this back into the equation:
\[ 20.4 \times \frac{25}{1000} \times x = 382.5 \]

### Step 4: Calculate \(20.4 \times \frac{25}{1000}\)
Now calculate \(20.4 \times \frac{25}{1000}\):
\[ 20.4 \times 25 = 510 \]
So,
\[ \frac{510}{1000} \times x = 382.5 \]

### Step 5: Clear the fraction
Multiply both sides by \(1000\) to eliminate the denominator:
\[ 510x = 382500 \]

### Step 6: Solve for \(x\)
Now, divide both sides by \(510\):
\[ x = \frac{382500}{510} \]

### Step 7: Perform the division
Calculating the division:
\[ x = 750 \]

Thus, the value of \(x\) is \(750\).

### Final Answer:
The value of \(x\) is \(750\).

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