Jhons income is 20% more than that of Mr thomas. How much per cent is the incomme of Mr thomes less than that of jhon?

Answer

To solve the problem step by step, we will follow the logical reasoning based on the information given:

### Step 1: Define Mr. Thomas's Income
Let the income of Mr. Thomas be represented as \( x \).

### Step 2: Calculate John’s Income
Since John's income is 20% more than Mr. Thomas's income, we can calculate John's income as follows:
\[ \text{John's Income} = x + 20\% \text{ of } x = x + \frac{20}{100} \times x = x + 0.2x = 1.2x \]

### Step 3: Find the Difference in Income
Next, we need to find out how much less Mr. Thomas's income is compared to John's income. We do this by subtracting Mr. Thomas's income from John's income:
\[ \text{Difference} = \text{John's Income} - \text{Mr. Thomas's Income} = 1.2x - x = 0.2x \]

### Step 4: Calculate the Percentage Decrease
To find out how much percent Mr. Thomas's income is less than John's income, we use the formula for percentage decrease:
\[ \text{Percentage Decrease} = \left(\frac{\text{Difference}}{\text{John's Income}}\right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Decrease} = \left(\frac{0.2x}{1.2x}\right) \times 100 \]

### Step 5: Simplify the Expression
Now we simplify the expression:
\[ \text{Percentage Decrease} = \left(\frac{0.2}{1.2}\right) \times 100 = \frac{2}{12} \times 100 = \frac{100}{6} \]

### Step 6: Final Calculation
Now we can simplify \( \frac{100}{6} \):
\[ \frac{100}{6} \approx 16.67\% \]

Thus, Mr. Thomas's income is approximately **16.67% less than John's income**.

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