What approximate value should come in the place of (?) mark :
?% of 420.01 + `(12.01)^(2)` = 24.01% of 1649.99

Options

A. 54
B. 60
C. 64
D. 50

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Understand the equation
We need to find the approximate value of the question mark (?) in the equation:
\[ ?\% \text{ of } 420.01 + (12.01)^2 = 24.01\% \text{ of } 1649.99 \]

### Step 2: Approximate the values
We can approximate the numbers for easier calculations:
- \( 420.01 \approx 420 \)
- \( 12.01 \approx 12 \)
- \( 24.01\% \approx 24\% \)
- \( 1649.99 \approx 1650 \)

So, the equation simplifies to:
\[ ?\% \text{ of } 420 + 12^2 = 24\% \text{ of } 1650 \]

### Step 3: Calculate \( 12^2 \)
Calculate \( 12^2 \):
\[ 12^2 = 144 \]

### Step 4: Calculate \( 24\% \text{ of } 1650 \)
Calculate \( 24\% \text{ of } 1650 \):
\[ 24\% \text{ of } 1650 = \frac{24}{100} \times 1650 = \frac{24 \times 1650}{100} \]
\[ = \frac{39600}{100} = 396 \]

### Step 5: Set up the equation
Now we can set up the equation:
\[ ?\% \text{ of } 420 + 144 = 396 \]

### Step 6: Isolate the percentage term
Subtract 144 from both sides:
\[ ?\% \text{ of } 420 = 396 - 144 \]
\[ ?\% \text{ of } 420 = 252 \]

### Step 7: Convert percentage to fraction
Convert the percentage to a fraction:
\[ \frac{?}{100} \times 420 = 252 \]

### Step 8: Solve for ?
Multiply both sides by 100:
\[ ? \times 420 = 25200 \]

Now divide both sides by 420:
\[ ? = \frac{25200}{420} \]

### Step 9: Simplify the fraction
To simplify:
\[ ? = 60 \]

### Final Answer
The approximate value that should come in place of the (?) mark is:
\[ \boxed{60} \]

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