`2/3` of a number is 20 less than the original number. Find the number.

Options

A. `40`
B. `50`
C. `60`
D. `70`

Answer

To solve the problem step by step, we will first set up an equation based on the information given in the question.

### Step-by-Step Solution:

1. **Define the Variable:**
Let the unknown number be represented by \( x \).

2. **Translate the Problem into an Equation:**
According to the problem, \( \frac{2}{3} \) of the number \( x \) is equal to 20 less than the original number \( x \). This can be expressed as:
\[ \frac{2}{3}x = x - 20 \]

3. **Eliminate the Fraction:**
To eliminate the fraction, multiply every term in the equation by 3:
\[ 3 \cdot \frac{2}{3}x = 3(x - 20) \]
This simplifies to:
\[ 2x = 3x - 60 \]

4. **Rearrange the Equation:**
Now, we will rearrange the equation to isolate \( x \). Subtract \( 3x \) from both sides:
\[ 2x - 3x = -60 \]
This simplifies to:
\[ -x = -60 \]

5. **Solve for \( x \):**
Multiply both sides by -1 to solve for \( x \):
\[ x = 60 \]

6. **Conclusion:**
The original number is \( 60 \).