What value will come in place of question mark (?) in the questions given below?
`2/3xx4/6 " of " 9/16 xx 5/8 = 5/?`

Options

A. 32
B. 8
C. 5
D. 0

Answer

To solve the equation \( \frac{2}{3} \times \frac{4}{6} \text{ of } \frac{9}{16} \times \frac{5}{8} = \frac{5}{?} \), we will follow these steps:

### Step 1: Understand the equation
The term "of" in the equation indicates multiplication. Therefore, we can rewrite the equation as:
\[ \frac{2}{3} \times \frac{4}{6} \times \frac{9}{16} \times \frac{5}{8} = \frac{5}{?} \]

### Step 2: Simplify the left side of the equation
We will multiply the fractions on the left side:
\[ \frac{2 \times 4 \times 9 \times 5}{3 \times 6 \times 16 \times 8} \]

### Step 3: Calculate the numerator
Calculating the numerator:
\[ 2 \times 4 = 8 \]
\[ 8 \times 9 = 72 \]
\[ 72 \times 5 = 360 \]
So, the numerator is \( 360 \).

### Step 4: Calculate the denominator
Calculating the denominator:
\[ 3 \times 6 = 18 \]
\[ 18 \times 16 = 288 \]
\[ 288 \times 8 = 2304 \]
So, the denominator is \( 2304 \).

### Step 5: Write the left side fraction
Now we can write the left side as:
\[ \frac{360}{2304} \]

### Step 6: Set the equation
Now we have:
\[ \frac{360}{2304} = \frac{5}{?} \]

### Step 7: Cross-multiply to solve for ?
Cross-multiplying gives us:
\[ 360 \times ? = 5 \times 2304 \]

### Step 8: Calculate \( 5 \times 2304 \)
Calculating \( 5 \times 2304 \):
\[ 5 \times 2304 = 11520 \]

### Step 9: Solve for ?
Now we have:
\[ 360 \times ? = 11520 \]
To find \( ? \), divide both sides by 360:
\[ ? = \frac{11520}{360} \]

### Step 10: Simplify \( \frac{11520}{360} \)
Calculating \( \frac{11520}{360} \):
\[ ? = 32 \]

### Conclusion
Thus, the value that will come in place of the question mark (?) is \( 32 \).