What value will come in place of the question mark (?) in each of the following questions ?
`1/6 of 11/3 of 36/77 of 7/15 of?=84`

Options

A. 640
B. 630
C. 650
D. 635

Answer

To solve the equation \( \frac{1}{6} \times \frac{11}{3} \times \frac{36}{77} \times \frac{7}{15} \times ? = 84 \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \frac{1}{6} \times \frac{11}{3} \times \frac{36}{77} \times \frac{7}{15} \times ? = 84 \]

### Step 2: Combine the fractions
We can combine the fractions on the left side:
\[ ? = 84 \div \left( \frac{1}{6} \times \frac{11}{3} \times \frac{36}{77} \times \frac{7}{15} \right) \]

### Step 3: Calculate the product of the fractions
Now we will calculate the product:
\[ \frac{1}{6} \times \frac{11}{3} \times \frac{36}{77} \times \frac{7}{15} \]

Calculating each step:
- First, calculate \( \frac{1}{6} \times \frac{11}{3} = \frac{11}{18} \)
- Next, calculate \( \frac{11}{18} \times \frac{36}{77} = \frac{11 \times 36}{18 \times 77} = \frac{396}{1386} \)
- Simplifying \( \frac{396}{1386} \) gives \( \frac{22}{77} \) (after dividing both numerator and denominator by 18).
- Now, calculate \( \frac{22}{77} \times \frac{7}{15} = \frac{22 \times 7}{77 \times 15} = \frac{154}{1155} \)
- Simplifying \( \frac{154}{1155} \) gives \( \frac{22}{165} \) (after dividing both numerator and denominator by 7).

### Step 4: Substitute back into the equation
Now we substitute back into the equation:
\[ ? = 84 \div \frac{22}{165} \]

### Step 5: Simplify the division
To divide by a fraction, we multiply by its reciprocal:
\[ ? = 84 \times \frac{165}{22} \]

### Step 6: Calculate the value
Now we simplify:
\[ ? = 84 \times \frac{165}{22} = 84 \times 7.5 = 630 \]

### Final Answer
Thus, the value that comes in place of the question mark (?) is:
\[ \boxed{630} \]