A number is such, that when it is multiplied by 3, it gives another number which' is- as much above from 116 as the original number itself is below 116. What is `40%` of the original number?

Options

A. 23.2
B. 24.8
C. 20
D. 20.8

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Original Number
Let the original number be represented as \( x \).

### Step 2: Set Up the Equation
According to the problem, when the original number \( x \) is multiplied by 3, it gives another number \( 3x \). This number \( 3x \) is as much above 116 as the original number \( x \) is below 116.

This can be expressed mathematically as:
\[ 3x - 116 = 116 - x \]

### Step 3: Simplify the Equation
Now, we will simplify the equation:
\[ 3x - 116 = 116 - x \]
Adding \( x \) to both sides gives:
\[ 3x + x - 116 = 116 \]
This simplifies to:
\[ 4x - 116 = 116 \]
Now, add 116 to both sides:
\[ 4x = 116 + 116 \]
\[ 4x = 232 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 4 to find \( x \):
\[ x = \frac{232}{4} \]
Calculating this gives:
\[ x = 58 \]

### Step 5: Calculate 40% of the Original Number
To find 40% of the original number \( x \):
\[ 40\% \text{ of } x = \frac{40}{100} \times x = \frac{40}{100} \times 58 \]
This can be simplified to:
\[ = \frac{2320}{100} = 23.2 \]

### Final Answer
Thus, 40% of the original number is:
\[ \boxed{23.2} \]

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