Find the value of question mark (?) in the following questions given below
`(1)/(164)-: (84)/(?) = (1)/(16) xx (1)/(287)`

Options

A. 3
B. 4
C. 5
D. 6

Answer

To solve the equation \(\frac{1}{164} \div \frac{84}{?} = \frac{1}{16} \times \frac{1}{287}\), we can follow these steps:

### Step 1: Rewrite the Division as Multiplication
We can rewrite the division of fractions as multiplication by the reciprocal. Thus, we have:
\[ \frac{1}{164} \times \frac{?}{84} = \frac{1}{16} \times \frac{1}{287} \]

### Step 2: Simplify the Right Side
Now, calculate the right side:
\[ \frac{1}{16} \times \frac{1}{287} = \frac{1}{16 \times 287} = \frac{1}{4592} \]

### Step 3: Set Up the Equation
Now our equation looks like this:
\[ \frac{1}{164} \times \frac{?}{84} = \frac{1}{4592} \]

### Step 4: Cross-Multiply
To eliminate the fractions, we can cross-multiply:
\[ 1 \times ? = 84 \times \frac{164}{4592} \]

### Step 5: Calculate the Right Side
Now we need to calculate \(84 \times \frac{164}{4592}\). First, simplify \(\frac{164}{4592}\):
\[ \frac{164}{4592} = \frac{164 \div 4}{4592 \div 4} = \frac{41}{1148} \]
Now multiply:
\[ 84 \times \frac{41}{1148} = \frac{84 \times 41}{1148} \]

### Step 6: Simplify the Numerator
Calculating \(84 \times 41\):
\[ 84 \times 41 = 3444 \]
So we have:
\[ ? = \frac{3444}{1148} \]

### Step 7: Simplify the Fraction
Now simplify \(\frac{3444}{1148}\):
\[ \frac{3444 \div 4}{1148 \div 4} = \frac{861}{287} \]

### Step 8: Final Result
Thus, the value of the question mark (?) is:
\[ ? = 861 \]