Income of x is greater than income of y by 25%. Income of y is how many percent lesser than that of x?

Options

A. `25%`
B. `30%`
C. `20%`
D. `22%`

Answer

To solve the problem, we need to find out how much lesser the income of Y is compared to the income of X, given that the income of X is greater than that of Y by 25%.

### Step-by-Step Solution:

1. **Define the Income of Y**:
Let's assume the income of Y is \( Y = 100 \) (this is a convenient choice for calculation).

**Hint**: Start by assigning a value to Y to simplify calculations.

2. **Calculate the Income of X**:
Since the income of X is greater than that of Y by 25%, we can express the income of X as:
\[ X = Y + 0.25Y = 1.25Y \]
Substituting \( Y = 100 \):
\[ X = 1.25 \times 100 = 125 \]

**Hint**: Use the percentage increase formula to find X based on Y.

3. **Determine How Much Lesser Y is Compared to X**:
To find how much lesser Y is than X, we calculate the difference between X and Y:
\[ \text{Difference} = X - Y = 125 - 100 = 25 \]

**Hint**: Subtract Y from X to find the absolute difference.

4. **Calculate the Percentage Difference**:
Now, we need to find what percentage this difference (25) is of X (125):
\[ \text{Percentage lesser} = \left( \frac{\text{Difference}}{X} \right) \times 100 = \left( \frac{25}{125} \right) \times 100 \]
Simplifying this:
\[ \text{Percentage lesser} = \left( \frac{1}{5} \right) \times 100 = 20\% \]

**Hint**: Use the formula for percentage to express the difference relative to X.

### Final Answer:
The income of Y is 20% lesser than that of X.