A number is such that when it is multiplied by 7, it gives another number which is as much above 260 as the original number itself is below 260. What is `32%` of the original number?

Options

A. 21.2
B. 18.8
C. 20.5
D. 20.8

Answer

To solve the problem step by step, let's denote the original number as \( x \).

### Step 1: Set up the equation based on the problem statement.
According to the problem, when the original number \( x \) is multiplied by 7, the result is a number that is as much above 260 as \( x \) is below 260.

This can be expressed mathematically as:
\[ 7x = 260 + (260 - x) \]

### Step 2: Simplify the equation.
Now, let's simplify the equation:
\[ 7x = 260 + 260 - x \]
\[ 7x = 520 - x \]

### Step 3: Combine like terms.
Next, add \( x \) to both sides of the equation to combine the \( x \) terms:
\[ 7x + x = 520 \]
\[ 8x = 520 \]

### Step 4: Solve for \( x \).
Now, divide both sides by 8 to find \( x \):
\[ x = \frac{520}{8} \]
\[ x = 65 \]

### Step 5: Calculate 32% of the original number.
Now that we have the original number \( x = 65 \), we need to find 32% of \( x \):
\[ 32\% \text{ of } x = \frac{32}{100} \times 65 \]
\[ = 0.32 \times 65 \]
\[ = 20.8 \]

### Final Answer:
Thus, 32% of the original number is \( 20.8 \).

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