What approximate value should come in the place of question mark in following question.
`(312.07)/(?) + (12.99)^(2) = 20.01% "of 909.99"`

Options

A. None of these
B. 48
C. 6
D. 24

Answer

To solve the equation \( \frac{312.07}{?} + (12.99)^2 = 20.01\% \text{ of } 909.99 \), we will follow these steps:

### Step 1: Approximate the values
First, we can approximate the numbers for easier calculations:
- \( 312.07 \) can be approximated to \( 312 \).
- \( 12.99 \) can be approximated to \( 13 \).
- \( 20.01\% \) can be approximated to \( 20\% \).

So, our equation becomes:
\[ \frac{312}{?} + (13)^2 = 20\% \text{ of } 909.99 \]

### Step 2: Calculate \( (13)^2 \)
Now, calculate \( (13)^2 \):
\[ (13)^2 = 169 \]

### Step 3: Calculate \( 20\% \text{ of } 909.99 \)
Next, we calculate \( 20\% \text{ of } 909.99 \):
\[ 20\% \text{ of } 909.99 = \frac{20}{100} \times 909.99 = 0.2 \times 909.99 \approx 182 \]

### Step 4: Substitute values into the equation
Now, substitute the values back into the equation:
\[ \frac{312}{?} + 169 = 182 \]

### Step 5: Isolate \( \frac{312}{?} \)
To isolate \( \frac{312}{?} \), subtract \( 169 \) from both sides:
\[ \frac{312}{?} = 182 - 169 \]
\[ \frac{312}{?} = 13 \]

### Step 6: Cross-multiply to find \( ? \)
Now, cross-multiply to solve for \( ? \):
\[ 312 = 13 \times ? \]
\[ ? = \frac{312}{13} \]

### Step 7: Calculate \( ? \)
Now, calculate \( \frac{312}{13} \):
\[ ? \approx 24 \]

Thus, the approximate value that should come in place of the question mark is \( 24 \).

### Final Answer
The answer is \( 24 \).

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