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

Options

A. 0.25
B. 0.3
C. 0.2
D. 0.22

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step-by-Step Solution:

**Step 1: Define the incomes of X and Y.**
Let's assume the income of Y is 100 units (this is a convenient base for calculations).

**Step 2: Calculate the income of X.**
Since the income of X is greater than the income of Y by 25%, we can calculate the income of X as follows:
\[ \text{Income of X} = \text{Income of Y} + 25\% \text{ of Income of Y} \]
\[ \text{Income of X} = 100 + 0.25 \times 100 = 100 + 25 = 125 \]

**Step 3: Determine how much lesser the income of Y is compared to X.**
Now we need to find out how much lesser the income of Y (100) is compared to the income of X (125). We can calculate this difference:
\[ \text{Difference} = \text{Income of X} - \text{Income of Y} = 125 - 100 = 25 \]

**Step 4: Calculate the percentage by which Y's income is lesser than X's income.**
To find out how many percent lesser Y's income is than X's income, we use the formula:
\[ \text{Percentage lesser} = \left( \frac{\text{Difference}}{\text{Income of X}} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage lesser} = \left( \frac{25}{125} \right) \times 100 \]
\[ \text{Percentage lesser} = \left( \frac{1}{5} \right) \times 100 = 20\% \]

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

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