What approximate value should come in place of question mark(?) in the following questions?
`?%of(sqrt((15.85))xx25.02+219.85)=224.11`

Options

A. 50
B. 45
C. 80
D. 70

Answer

To solve the equation \( ?\% \text{ of } (\sqrt{15.85} \times 25.02 + 219.85) = 224.11 \), we will follow these steps:

### Step 1: Approximate the values
1. Calculate the approximate value of \( \sqrt{15.85} \).
- \( \sqrt{15.85} \approx 4 \) (since \( \sqrt{16} = 4 \)).

2. Approximate \( 25.02 \) to \( 25 \).
3. Approximate \( 219.85 \) to \( 220 \).
4. Approximate \( 224.11 \) to \( 224 \).

### Step 2: Substitute the approximated values into the equation
Now, substituting the approximated values into the equation:
\[ ? \% \text{ of } (4 \times 25 + 220) = 224 \]

### Step 3: Calculate the expression inside the parentheses
1. Calculate \( 4 \times 25 \):
- \( 4 \times 25 = 100 \).

2. Add \( 100 \) and \( 220 \):
- \( 100 + 220 = 320 \).

### Step 4: Rewrite the equation
Now, we rewrite the equation with the calculated values:
\[ ? \% \text{ of } 320 = 224 \]

### Step 5: Convert percentage to decimal
Convert \( ?\% \) to decimal form:
\[ \frac{?}{100} \times 320 = 224 \]

### Step 6: Solve for ?
To isolate \( ? \), we rearrange the equation:
\[ ? = \frac{224 \times 100}{320} \]

### Step 7: Calculate the value of ?
1. Calculate \( \frac{224 \times 100}{320} \):
- First, simplify \( \frac{224}{320} \):
- \( \frac{224}{32} = 7 \) and \( \frac{320}{32} = 10 \).
- Thus, \( \frac{224}{320} = \frac{7}{10} \).

2. Now multiply by \( 100 \):
- \( ? = 7 \times 10 = 70 \).

### Final Answer
The approximate value that should come in place of the question mark (?) is \( 70 \).

---