When a number is increased by 105, it becomes `135%` of itself. What is the number ?

Options

A. `450`
B. `300`
C. `600`
D. `400`

Answer

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

### Step 1: Set up the equation
According to the problem, when the number \( x \) is increased by 105, it becomes 135% of itself. This can be expressed mathematically as:
\[ x + 105 = 1.35x \]

### Step 2: Rearrange the equation
To isolate \( x \), we can rearrange the equation:
\[ x + 105 = 1.35x \]
Subtract \( x \) from both sides:
\[ 105 = 1.35x - x \]
This simplifies to:
\[ 105 = 0.35x \]

### Step 3: Solve for \( x \)
Now, we can solve for \( x \) by dividing both sides by 0.35:
\[ x = \frac{105}{0.35} \]

### Step 4: Calculate the value
Now, we perform the division:
\[ x = 105 \div 0.35 = 300 \]

### Conclusion
Thus, the number is:
\[ \boxed{300} \]

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