What approximate value will come in place of question mark (?) in the following questions. (You are not expected to find the exact value)
59.9% of 319.94 + 9.99% of 1600.01 = - 177 + `(?)^(2)`

Options

A. 26
B. 33
C. 23
D. 20

Answer

To solve the equation \( 59.9\% \text{ of } 319.94 + 9.99\% \text{ of } 1600.01 = -177 + (?)^2 \), we will approximate the values and then solve for the question mark.

### Step-by-Step Solution:

1. **Approximate the Percentages**:
- \( 59.9\% \) can be approximated to \( 60\% \).
- \( 9.99\% \) can be approximated to \( 10\% \).

2. **Approximate the Values**:
- \( 319.94 \) can be approximated to \( 320 \).
- \( 1600.01 \) can be approximated to \( 1600 \).

3. **Calculate the Approximated Values**:
- Calculate \( 60\% \text{ of } 320 \):
\[ 60\% \text{ of } 320 = \frac{60}{100} \times 320 = 192 \]
- Calculate \( 10\% \text{ of } 1600 \):
\[ 10\% \text{ of } 1600 = \frac{10}{100} \times 1600 = 160 \]

4. **Combine the Results**:
- Now, add the two results:
\[ 192 + 160 = 352 \]

5. **Set Up the Equation**:
- Now, we can set up the equation:
\[ 352 = -177 + (?)^2 \]

6. **Isolate the Square Term**:
- Add \( 177 \) to both sides:
\[ 352 + 177 = (?)^2 \]
\[ 529 = (?)^2 \]

7. **Find the Square Root**:
- To find \( ? \), take the square root of both sides:
\[ ? = \sqrt{529} \]
- Since \( 23^2 = 529 \), we have:
\[ ? = 23 \]

### Final Answer:
The approximate value that will come in place of the question mark (?) is **23**.