What approximate value will come in place of question mark (?) in the following question ?
`(5)/(7) xx (42)/(201) xx (?)/(4) =7`

Options

A. 216
B. 188
C. 166
D. 140

Answer

To solve the equation \(\frac{5}{7} \times \frac{42}{201} \times \frac{?}{4} = 7\), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \frac{5}{7} \times \frac{42}{201} \times \frac{x}{4} = 7 \]

### Step 2: Simplify the fractions
First, we can simplify \(\frac{42}{201}\):
\[ \frac{42}{201} = \frac{42 \div 3}{201 \div 3} = \frac{14}{67} \]
So, we can rewrite the equation as:
\[ \frac{5}{7} \times \frac{14}{67} \times \frac{x}{4} = 7 \]

### Step 3: Multiply the fractions
Now, we multiply the fractions:
\[ \frac{5 \times 14 \times x}{7 \times 67 \times 4} = 7 \]
This simplifies to:
\[ \frac{70x}{1888} = 7 \]

### Step 4: Cross-multiply
Next, we cross-multiply to eliminate the fraction:
\[ 70x = 7 \times 1888 \]
Calculating \(7 \times 1888\):
\[ 7 \times 1888 = 13116 \]
So we have:
\[ 70x = 13116 \]

### Step 5: Solve for \(x\)
Now, we divide both sides by 70 to find \(x\):
\[ x = \frac{13116}{70} \]
Calculating the division:
\[ x \approx 187.37 \]

### Step 6: Approximate the value
The approximate value of \(x\) is around 188.

### Final Answer
Thus, the approximate value that comes in place of the question mark (?) is:
\[ \boxed{188} \]

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