If the price of an item A is `25%` less than that of the item B. How much percent is the price of B more than that of A?

Options

A. `50%`
B. `33 1/3%`
C. `16 2/3%`
D. `25%`

Answer

To find out how much percent the price of item B is more than that of item A, we can follow these steps:

### Step 1: Define the prices of items A and B
Let the price of item B be represented as \( P_B \). Since item A is 25% less than item B, we can express the price of item A as:
\[ P_A = P_B - 0.25 \times P_B = 0.75 \times P_B \]

### Step 2: Calculate the difference in prices
Now, we need to find the difference between the prices of items B and A:
\[ \text{Difference} = P_B - P_A = P_B - 0.75 \times P_B = 0.25 \times P_B \]

### Step 3: Calculate the percentage increase of B over A
To find out how much percent the price of B is more than the price of A, we use the formula for percentage increase:
\[ \text{Percentage Increase} = \left( \frac{\text{Difference}}{P_A} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{0.25 \times P_B}{0.75 \times P_B} \right) \times 100 \]

### Step 4: Simplify the expression
The \( P_B \) cancels out:
\[ \text{Percentage Increase} = \left( \frac{0.25}{0.75} \right) \times 100 \]
\[ \text{Percentage Increase} = \left( \frac{1}{3} \right) \times 100 = 33.33\% \]

### Conclusion
Thus, the price of item B is approximately \( 33.33\% \) more than that of item A.