40% of a number when added to the square of the same number, then it is increased to 40% of itself the actual number is :

Options

A. a. 175
B. b. 400
C. c. 0 or 1
D. d. 120

Answer

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

### Step 1: Write the equation based on the problem statement.
The problem states that 40% of a number \( x \) when added to the square of the same number \( x \) results in an increase to 40% of itself. We can express this mathematically as follows:

\[ 0.4x + x^2 = 0.4x + x \]

### Step 2: Simplify the equation.
Next, we can simplify the equation by subtracting \( 0.4x \) from both sides:

\[ x^2 = x \]

### Step 3: Rearrange the equation.
Now, we can rearrange the equation to bring all terms to one side:

\[ x^2 - x = 0 \]

### Step 4: Factor the equation.
We can factor the left-hand side:

\[ x(x - 1) = 0 \]

### Step 5: Solve for \( x \).
Setting each factor to zero gives us the possible solutions:

1. \( x = 0 \)
2. \( x - 1 = 0 \) which gives \( x = 1 \)

### Conclusion:
The actual number can be either \( 0 \) or \( 1 \).

Thus, the final answer is:
- The actual number is \( 0 \) or \( 1 \).

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