What approximate value will come in place of the questions mark(?) in the following questions? (You are not expected to calculate the exact value)
`(24.95/9.88)^2xx1010/624+51/499=?`

Options

A. 10.1
B. 15.1
C. 5.3
D. 20

Answer

To solve the equation \( \left( \frac{24.95}{9.88} \right)^2 \times \frac{1010}{624} + \frac{51}{499} = ? \), we will approximate the values to make the calculations easier.

### Step-by-Step Solution:

1. **Approximate the Values**:
- Approximate \( 24.95 \) to \( 25 \).
- Approximate \( 9.88 \) to \( 10 \).
- Approximate \( 1010 \) to \( 1000 \).
- Approximate \( 624 \) to \( 625 \).
- Approximate \( 51 \) to \( 50 \).
- Approximate \( 499 \) to \( 500 \).

So, the expression becomes:
\[ \left( \frac{25}{10} \right)^2 \times \frac{1000}{625} + \frac{50}{500} \]

2. **Simplify the Fractions**:
- Calculate \( \frac{25}{10} = 2.5 \).
- Therefore, \( \left( \frac{25}{10} \right)^2 = (2.5)^2 = 6.25 \).
- Now, calculate \( \frac{1000}{625} \):
\[ \frac{1000}{625} = \frac{1000 \div 125}{625 \div 125} = \frac{8}{5} = 1.6 \]

3. **Multiply the Results**:
- Now, multiply \( 6.25 \) by \( 1.6 \):
\[ 6.25 \times 1.6 = 10 \]

4. **Calculate the Second Fraction**:
- Now, calculate \( \frac{50}{500} \):
\[ \frac{50}{500} = \frac{1}{10} = 0.1 \]

5. **Add the Results**:
- Finally, add \( 10 \) and \( 0.1 \):
\[ 10 + 0.1 = 10.1 \]

Thus, the approximate value that comes in place of the question mark is \( \boxed{10.1} \).