What will come in place of (?) in the following questions ?
`(?)^(3) + (9)^(2) = (12)^(3) - 35% "of 1800" - 80% "of 360"`

Options

A. 14
B. 12
C. 9
D. 6

Answer

To solve the equation \( (?)^3 + 9^2 = 12^3 - 35\% \text{ of } 1800 - 80\% \text{ of } 360 \), we will follow these steps:

### Step 1: Calculate \( 9^2 \) and \( 12^3 \)

First, we calculate \( 9^2 \) and \( 12^3 \):

\[ 9^2 = 81 \]

\[ 12^3 = 1728 \]

### Step 2: Calculate \( 35\% \text{ of } 1800 \)

Next, we calculate \( 35\% \text{ of } 1800 \):

\[ 35\% \text{ of } 1800 = \frac{35}{100} \times 1800 = 630 \]

### Step 3: Calculate \( 80\% \text{ of } 360 \)

Now, we calculate \( 80\% \text{ of } 360 \):

\[ 80\% \text{ of } 360 = \frac{80}{100} \times 360 = 288 \]

### Step 4: Substitute values into the equation

Now we substitute these values back into the equation:

\[ (?)^3 + 81 = 1728 - 630 - 288 \]

### Step 5: Simplify the right side

Now we simplify the right side:

\[ 1728 - 630 = 1098 \]
\[ 1098 - 288 = 810 \]

So, we have:

\[ (?)^3 + 81 = 810 \]

### Step 6: Isolate \( (?)^3 \)

Now, we isolate \( (?)^3 \):

\[ (?)^3 = 810 - 81 \]
\[ (?)^3 = 729 \]

### Step 7: Find the value of \( ? \)

Now, we need to find the cube root of 729:

\[ ? = \sqrt[3]{729} = 9 \]

Thus, the value that comes in place of \( ? \) is \( 9 \).

### Final Answer

The answer is \( 9 \).

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