What will come in place of question mark (?) in the following questions ?
`(1261 xx ?)/(8000) - (3 xx ?)/(20) = 152.50`

Options

A. 18000
B. 22000
C. 24000
D. None of these

Answer

To solve the equation \((1261 \times x)/(8000) - (3 \times x)/(20) = 152.50\), we will follow these steps:

### Step 1: Rewrite the equation
We start with the original equation:
\[ \frac{1261x}{8000} - \frac{3x}{20} = 152.50 \]
To eliminate the decimal, we can multiply the entire equation by 100:
\[ 100 \left(\frac{1261x}{8000}\right) - 100 \left(\frac{3x}{20}\right) = 100 \times 152.50 \]
This simplifies to:
\[ \frac{126100x}{8000} - \frac{300x}{20} = 15250 \]

### Step 2: Simplify the fractions
Next, we simplify the fractions:
\[ \frac{126100x}{8000} - \frac{300x}{20} = 15250 \]
The second term can be simplified:
\[ \frac{300x}{20} = 15x \]
So the equation now looks like:
\[ \frac{126100x}{8000} - 15x = 15250 \]

### Step 3: Find a common denominator
To combine the terms on the left, we need a common denominator. The common denominator for \(8000\) and \(1\) (since \(15x\) can be written as \(\frac{15x \times 8000}{8000}\)) is \(8000\):
\[ \frac{126100x - 15x \times 8000}{8000} = 15250 \]

### Step 4: Multiply both sides by 8000
Now, we multiply both sides of the equation by \(8000\) to eliminate the fraction:
\[ 126100x - 120000x = 15250 \times 8000 \]

### Step 5: Simplify the equation
This simplifies to:
\[ 6100x = 122000000 \]

### Step 6: Solve for \(x\)
Now, divide both sides by \(6100\):
\[ x = \frac{122000000}{6100} \]

### Step 7: Calculate the value of \(x\)
Calculating the right-hand side:
\[ x = 20000 \]

Thus, the value that comes in place of the question mark (?) is \(20000\).

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