If A's salary is 30% more than that of B, then how much per cent is B's salary less than that of A's?

Options

A. `30%`
B. `25%`
C. `23(1)/(3)%`
D. `33(1)/(3)%`

Answer

To solve the problem step by step, we will first define the salaries of A and B and then calculate the required percentage.

### Step 1: Define the salaries
Let B's salary be represented as \( B \). Since A's salary is 30% more than B's salary, we can express A's salary as:
\[ A = B + 0.30B = 1.30B \]

### Step 2: Find the difference in salaries
Now, we need to find out how much less B's salary is than A's salary. The difference between A's salary and B's salary is:
\[ A - B = 1.30B - B = 0.30B \]

### Step 3: Calculate the percentage difference
To find out how much percent B's salary is less than A's salary, we use the formula for percentage difference:
\[ \text{Percentage} = \left( \frac{\text{Difference}}{\text{A's Salary}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage} = \left( \frac{0.30B}{1.30B} \right) \times 100 \]

### Step 4: Simplify the expression
The \( B \) in the numerator and denominator cancels out:
\[ \text{Percentage} = \left( \frac{0.30}{1.30} \right) \times 100 \]

### Step 5: Calculate the fraction
Now, we can simplify \( \frac{0.30}{1.30} \):
\[ \frac{0.30}{1.30} = \frac{30}{130} = \frac{3}{13} \]

### Step 6: Convert to percentage
Now, we convert \( \frac{3}{13} \) to a percentage:
\[ \text{Percentage} = \frac{3}{13} \times 100 \approx 23.0769 \]
Rounding this gives us approximately:
\[ \text{Percentage} \approx 23.08\% \]

### Final Answer
Thus, B's salary is approximately **23.08% less than A's salary**.

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