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 solve the problem step by step, we can follow these instructions:

### Step 1: Define the prices of items A and B
Let the price of item B be \( P_B = 100 \) (we can assume any value, but 100 makes calculations easier).

### Step 2: Calculate the price of item A
Since the price of item A is 25% less than that of item B, we can calculate the price of item A as follows:
\[ P_A = P_B - (25\% \text{ of } P_B) = 100 - (0.25 \times 100) = 100 - 25 = 75 \]

### Step 3: Find the difference in prices
Now, we need to find out how much more the price of item B is compared to item A. We can calculate the difference:
\[ \text{Difference} = P_B - P_A = 100 - 75 = 25 \]

### Step 4: Calculate the percentage increase
To find out how much percent the price of B is more than that of A, we use the formula for percentage increase:
\[ \text{Percentage Increase} = \left( \frac{\text{Difference}}{P_A} \right) \times 100 = \left( \frac{25}{75} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage Increase} = \left( \frac{25}{75} \right) \times 100 = \frac{1}{3} \times 100 = 33.33\% \]

### Conclusion
Thus, the price of item B is \( 33 \frac{1}{3} \% \) more than that of item A.

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