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 can follow these steps:

### Step 1: Convert percentages to decimal form
Convert \(3.4\%\) and \(2.5\%\) into decimal form:
- \(3.4\% = \frac{3.4}{100} = 0.034\)
- \(2.5\% = \frac{2.5}{100} = 0.025\)

### Step 2: Substitute the percentages into the equation
Now, substitute these values into the equation:
\[ 0.034 \times 600 \times 0.025 \times x = 382.5 \]

### Step 3: Calculate \(3.4\%\) of \(600\)
Calculate \(0.034 \times 600\):
\[ 0.034 \times 600 = 20.4 \]

### Step 4: Substitute back into the equation
Now substitute this result back into the equation:
\[ 20.4 \times 0.025 \times x = 382.5 \]

### Step 5: Calculate \(2.5\%\) of \(x\)
Calculate \(20.4 \times 0.025\):
\[ 20.4 \times 0.025 = 0.51 \]

### Step 6: Rewrite the equation
Now the equation becomes:
\[ 0.51x = 382.5 \]

### Step 7: Solve for \(x\)
To find \(x\), divide both sides by \(0.51\):
\[ x = \frac{382.5}{0.51} \]

### Step 8: Perform the division
Calculate \(x\):
\[ x = 750 \]

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