What will come in place of question mark (?) in the following questions ?
`(? + 102.50)/(?) = ((21)/(20))^(2)`

Options

A. 950
B. 1200
C. 1000
D. 1050

Answer

To solve the equation \((? + 102.50)/(?) = ((21)/(20))^{2}\), we will denote the question mark as \(x\). Thus, we can rewrite the equation as:

\[ \frac{x + 102.50}{x} = \left(\frac{21}{20}\right)^{2} \]

### Step 1: Calculate \(\left(\frac{21}{20}\right)^{2}\)

First, we will calculate the right side of the equation:

\[ \left(\frac{21}{20}\right)^{2} = \frac{21^2}{20^2} = \frac{441}{400} \]

### Step 2: Rewrite the equation

Now, we can rewrite the equation as:

\[ \frac{x + 102.50}{x} = \frac{441}{400} \]

### Step 3: Cross-multiply

Next, we will cross-multiply to eliminate the fraction:

\[ 400(x + 102.50) = 441x \]

### Step 4: Distribute on the left side

Now, distribute \(400\) on the left side:

\[ 400x + 400 \times 102.50 = 441x \]

Calculating \(400 \times 102.50\):

\[ 400 \times 102.50 = 41000 \]

So, we have:

\[ 400x + 41000 = 441x \]

### Step 5: Rearrange the equation

Now, we will rearrange the equation to isolate \(x\):

\[ 41000 = 441x - 400x \]

This simplifies to:

\[ 41000 = 41x \]

### Step 6: Solve for \(x\)

Now, divide both sides by \(41\):

\[ x = \frac{41000}{41} \]

Calculating this gives:

\[ x = 1000 \]

### Final Answer

Thus, the value that comes in place of the question mark (?) is:

\[ \boxed{1000} \]

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