A number exceeds 20% of itself by 40. Find the number.

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the variable
Let the unknown number be represented by \( x \).

### Step 2: Write the equation based on the problem statement
According to the question, the number exceeds 20% of itself by 40. This can be expressed mathematically as:
\[ x = 0.2x + 40 \]

### Step 3: Convert 20% to a fraction
20% can be written as a fraction:
\[ 0.2 = \frac{20}{100} = \frac{1}{5} \]
So we can rewrite the equation as:
\[ x = \frac{1}{5}x + 40 \]

### Step 4: Rearrange the equation
To isolate \( x \), we need to move \( \frac{1}{5}x \) to the left side:
\[ x - \frac{1}{5}x = 40 \]

### Step 5: Combine like terms
To combine \( x \) and \( \frac{1}{5}x \), we can express \( x \) as \( \frac{5}{5}x \):
\[ \frac{5}{5}x - \frac{1}{5}x = 40 \]
This simplifies to:
\[ \frac{4}{5}x = 40 \]

### Step 6: Solve for \( x \)
To find \( x \), multiply both sides by the reciprocal of \( \frac{4}{5} \), which is \( \frac{5}{4} \):
\[ x = 40 \times \frac{5}{4} \]

### Step 7: Calculate the value
Calculating the right side:
\[ x = 40 \times \frac{5}{4} = 40 \times 1.25 = 50 \]

### Final Answer
Thus, the number is:
\[ \boxed{50} \]

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