What approximate value should come in place of the question mark (?) in the following questions ?
Note : (You are not expected to calculate the exact value.)
`10.11 xx 36.93 + sqrt(48.875) xx 19.99 = 99.931 xx sqrt(?)`

Options

A. 25
B. 144
C. 225
D. 900

Answer

To solve the equation \( 10.11 \times 36.93 + \sqrt{48.875} \times 19.99 = 99.931 \times \sqrt{?} \), we will approximate the values of each term to find the approximate value of the question mark.

### Step-by-Step Solution:

1. **Approximate the values:**
- Approximate \( 10.11 \) to \( 10 \).
- Approximate \( 36.93 \) to \( 37 \).
- Approximate \( 48.875 \) to \( 49 \).
- Approximate \( 19.99 \) to \( 20 \).
- Approximate \( 99.931 \) to \( 100 \).

So, we rewrite the equation as:
\[ 10 \times 37 + \sqrt{49} \times 20 = 100 \times \sqrt{?} \]

2. **Calculate the left-hand side:**
- Calculate \( 10 \times 37 = 370 \).
- Calculate \( \sqrt{49} = 7 \).
- Calculate \( 7 \times 20 = 140 \).

Now, add these two results:
\[ 370 + 140 = 510 \]

3. **Set the equation:**
Now we have:
\[ 510 = 100 \times \sqrt{?} \]

4. **Isolate \( \sqrt{?} \):**
Divide both sides by \( 100 \):
\[ \sqrt{?} = \frac{510}{100} = 5.1 \]

5. **Square both sides to find \( ? \):**
\[ ? = (5.1)^2 \]

6. **Calculate \( (5.1)^2 \):**
- \( 5.1 \times 5.1 = 26.01 \).

7. **Choose the closest option:**
The options given are 25, 144, 225, and 900. The closest approximate value to \( 26.01 \) is \( 25 \).

### Final Answer:
The approximate value that should come in place of the question mark (?) is **25**.