`2/3` of a number is less than the orignal number by 10. The original number is

Options

A. `30`
B. `36`
C. `45`
D. `60`

Answer

To solve the problem step by step, we need to set up an equation based on the information provided in the question.

### Step 1: Define the variable
Let the original number be \( x \).

### Step 2: Set up the equation
According to the problem, \( \frac{2}{3} \) of the number is less than the original number by 10. This can be expressed as:
\[ \frac{2}{3}x = x - 10 \]

### Step 3: Rearrange the equation
To solve for \( x \), we can rearrange the equation:
\[ \frac{2}{3}x + 10 = x \]

### Step 4: Eliminate the fraction
To eliminate the fraction, we can multiply every term by 3:
\[ 3 \cdot \left(\frac{2}{3}x\right) + 3 \cdot 10 = 3 \cdot x \]
This simplifies to:
\[ 2x + 30 = 3x \]

### Step 5: Isolate \( x \)
Now, we can isolate \( x \) by subtracting \( 2x \) from both sides:
\[ 30 = 3x - 2x \]
This simplifies to:
\[ 30 = x \]

### Step 6: Conclusion
Thus, the original number is:
\[ \boxed{30} \]