What approximate value should come in place of Question mark (?) in the following equation ?
`19.66% "of 144.87" - (266.47)/(118.84) xx (17)/(18.84) = ?^(3)`

Options

A. 5
B. 7
C. 0
D. 3

Answer

To solve the equation step by step, we will approximate the values and simplify the expression.

### Step 1: Approximate the values
We start with the expression:
\[ 19.66\% \text{ of } 144.87 - \frac{266.47}{118.84} \times \frac{17}{18.84} = ?^3 \]

1. **Approximate 19.66%**:
\[ 19.66 \approx 20 \]
So,
\[ 20\% = \frac{20}{100} = \frac{1}{5} \]

2. **Approximate 144.87**:
\[ 144.87 \approx 145 \]

### Step 2: Calculate 20% of 145
Now, we calculate:
\[ 20\% \text{ of } 145 = \frac{1}{5} \times 145 = 29 \]

### Step 3: Approximate the denominator
Next, we approximate the values in the second part of the expression:
1. **Approximate 266.47**:
\[ 266.47 \approx 266 \]

2. **Approximate 118.84**:
\[ 118.84 \approx 119 \]

3. **Approximate 18.84**:
\[ 18.84 \approx 19 \]

### Step 4: Calculate the fraction
Now we calculate:
\[ \frac{266}{119} \times \frac{17}{19} \]

### Step 5: Simplify the fraction
1. **Simplify \(\frac{266}{119}\)**:
- We can approximate \(266\) as \(17 \times 15.647\) and \(119\) as \(19 \times 6.263\), but for simplicity, we will just calculate:
\[ \frac{266}{119} \approx 2.24 \]

2. **Calculate \(\frac{17}{19} \approx 0.89\)**.

### Step 6: Multiply the fractions
Now, we multiply:
\[ 2.24 \times 0.89 \approx 2 \]

### Step 7: Combine the results
Now we combine the results from Step 2 and Step 6:
\[ 29 - 2 = 27 \]

### Step 8: Set the equation
Now we set the equation:
\[ 27 = ?^3 \]

### Step 9: Solve for ?
To find \(?\):
\[ ? = \sqrt[3]{27} = 3 \]

### Final Answer
Thus, the approximate value that should come in place of the question mark (?) is:
\[ ? = 3 \]