What well Centre in place of the question mark (?) in the following questions?
` % " of" 800 + (12)^2 = 504`

Options

A. 45
B. 40
C. 60
D. 55

Answer

To solve the equation given in the question, we need to find the value that will replace the question mark (?). The equation is:

\[ ? \% \text{ of } 800 + (12)^2 = 504 \]

Let's break this down step by step.

### Step 1: Convert the percentage to a fraction
The percentage can be expressed as a fraction. Therefore, we can rewrite the equation as:

\[ \frac{?}{100} \times 800 + (12)^2 = 504 \]

### Step 2: Calculate \( (12)^2 \)
Next, we calculate \( (12)^2 \):

\[ (12)^2 = 144 \]

### Step 3: Substitute back into the equation
Now, we substitute \( 144 \) back into the equation:

\[ \frac{?}{100} \times 800 + 144 = 504 \]

### Step 4: Isolate the term with the question mark
To isolate the term with the question mark, we subtract \( 144 \) from both sides:

\[ \frac{?}{100} \times 800 = 504 - 144 \]

Calculating the right side:

\[ 504 - 144 = 360 \]

So, we have:

\[ \frac{?}{100} \times 800 = 360 \]

### Step 5: Solve for the question mark
Now, we can solve for the question mark by multiplying both sides by \( 100 \) and then dividing by \( 800 \):

\[ ? \times 800 = 360 \times 100 \]

Calculating the right side:

\[ 360 \times 100 = 36000 \]

So, we have:

\[ ? \times 800 = 36000 \]

Now, divide both sides by \( 800 \):

\[ ? = \frac{36000}{800} \]

### Step 6: Simplify the fraction
Now we simplify \( \frac{36000}{800} \):

\[ ? = \frac{36000 \div 400}{800 \div 400} = \frac{90}{2} = 45 \]

### Conclusion
Thus, the value that replaces the question mark is:

\[ ? = 45 \]

### Final Answer
The answer is \( 45 \).

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