What value will come in place of question mark (?) in the questions given below?
`25% ` of 640 + ? % of 200 = 225

Options

A. 30.5
B. 32.5
C. 48
D. 65

Answer

To solve the equation \( 25\% \) of \( 640 + ?\% \) of \( 200 = 225 \), we can follow these steps:

### Step 1: Calculate \( 25\% \) of \( 640 \)
To find \( 25\% \) of \( 640 \), we can use the formula:
\[ \text{Percentage} = \frac{\text{Percentage Value}}{100} \times \text{Total Value} \]
So,
\[ 25\% \text{ of } 640 = \frac{25}{100} \times 640 = \frac{1}{4} \times 640 = 160 \]

### Step 2: Substitute the value into the equation
Now we substitute \( 160 \) back into the equation:
\[ 160 + ?\% \text{ of } 200 = 225 \]

### Step 3: Isolate the term with the question mark
To isolate \( ?\% \text{ of } 200 \), we subtract \( 160 \) from both sides:
\[ ?\% \text{ of } 200 = 225 - 160 \]
\[ ?\% \text{ of } 200 = 65 \]

### Step 4: Express \( ?\% \) in terms of \( 200 \)
Using the percentage formula again, we can express \( ?\% \) as:
\[ ?\% \text{ of } 200 = \frac{?}{100} \times 200 \]
Setting this equal to \( 65 \):
\[ \frac{?}{100} \times 200 = 65 \]

### Step 5: Solve for \( ? \)
To solve for \( ? \), we can multiply both sides by \( 100 \) and divide by \( 200 \):
\[ ? \times 200 = 65 \times 100 \]
\[ ? \times 200 = 6500 \]
\[ ? = \frac{6500}{200} \]
\[ ? = 32.5 \]

### Conclusion
The value that will come in place of the question mark (?) is \( 32.5 \).