If A's income is 12 % more than B's income, B's income is how much less than A's income?

Options

A. 12.7%
B. 11.7 %
C. 10.7%
D. 9.7%

Answer

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

### Step 1: Understand the relationship between A's and B's income
We know that A's income is 12% more than B's income.

### Step 2: Assume B's income
Let’s assume B's income is \( B = 100 \) (this makes calculations easier).

### Step 3: Calculate A's income
Since A's income is 12% more than B's income, we can calculate A's income as follows:
\[ A = B + 12\% \text{ of } B = 100 + 12\% \text{ of } 100 \]
Calculating 12% of 100:
\[ 12\% \text{ of } 100 = \frac{12}{100} \times 100 = 12 \]
So, A's income becomes:
\[ A = 100 + 12 = 112 \]

### Step 4: Calculate how much less B's income is than A's income
Now, we need to find out how much less B's income is compared to A's income:
\[ \text{Difference} = A - B = 112 - 100 = 12 \]

### Step 5: Calculate the percentage difference
To find out how much less B's income is than A's income in percentage terms, we use the formula:
\[ \text{Percentage difference} = \left( \frac{\text{Difference}}{A} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage difference} = \left( \frac{12}{112} \right) \times 100 \]
Calculating this:
\[ \text{Percentage difference} = \left( \frac{12}{112} \right) \times 100 = \frac{1200}{112} \approx 10.71\% \]

### Conclusion
Thus, B's income is approximately 10.71% less than A's income.