What value should come in place of question mark (?) in the following questions?
`((?)(9)/(4))/(324)=((?)(1)/(4))/(9)`

Options

A. 27
B. `(36)^(2)`
C. 6
D. 36

Explanation

To find the value that should come in place of the question mark (?) in the equation

\[ \frac{(?)(9)}{4} \div 324 = \frac{(?)(1)}{4} \div 9 \]

we can follow these steps:

### Step 1: Replace the question mark with a variable
Let’s denote the question mark as \( X \). The equation now becomes:

\[ \frac{X \cdot 9}{4} \div 324 = \frac{X \cdot 1}{4} \div 9 \]

### Step 2: Rewrite the division as multiplication
We can rewrite the division as multiplication by the reciprocal:

\[ \frac{X \cdot 9}{4} \cdot \frac{1}{324} = \frac{X \cdot 1}{4} \cdot \frac{1}{9} \]

This simplifies to:

\[ \frac{X \cdot 9}{4 \cdot 324} = \frac{X}{4 \cdot 9} \]

### Step 3: Simplify both sides
Now, we can simplify both sides of the equation:

Left side:

\[ \frac{X \cdot 9}{1296} \quad (\text{since } 4 \cdot 324 = 1296) \]

Right side:

\[ \frac{X}{36} \quad (\text{since } 4 \cdot 9 = 36) \]

So we have:

\[ \frac{X \cdot 9}{1296} = \frac{X}{36} \]

### Step 4: Cross-multiply
Cross-multiplying gives us:

\[ X \cdot 9 \cdot 36 = X \cdot 1296 \]

### Step 5: Simplify the equation
Assuming \( X \neq 0 \), we can divide both sides by \( X \):

\[ 9 \cdot 36 = 1296 \]

### Step 6: Calculate the left side
Calculating \( 9 \cdot 36 \):

\[ 9 \cdot 36 = 324 \]

### Step 7: Set the equation
Now we have:

\[ 324 = 1296 \]

### Step 8: Solve for X
Now we can solve for \( X \):

\[ X = \frac{1296}{324} \]

Calculating this gives:

\[ X = 4 \]

### Final Answer
Thus, the value that should come in place of the question mark (?) is:

\[ \boxed{6} \]