If the cost price of 120 mangoes is equal to the selling price of 100 mangoes, what is the profit percent in this transaction?

Options

A. 21%
B. 20%
C. 15%
D. 17%

Answer

To solve the problem, we need to find the profit percentage based on the given information about the cost price (CP) and selling price (SP) of mangoes.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
- The cost price (CP) of 120 mangoes is equal to the selling price (SP) of 100 mangoes.

2. **Let’s Assign Values:**
- Let the cost price of 1 mango be \( x \).
- Therefore, the cost price of 120 mangoes is \( 120x \).

3. **Finding the Selling Price:**
- Since the cost price of 120 mangoes is equal to the selling price of 100 mangoes, we can write:
\[ SP \text{ of 100 mangoes} = 120x \]
- Let the selling price of 1 mango be \( y \).
- Therefore, the selling price of 100 mangoes is \( 100y \).
- Setting these equal gives us:
\[ 100y = 120x \]

4. **Calculating the Selling Price per Mango:**
- From the equation \( 100y = 120x \), we can solve for \( y \):
\[ y = \frac{120x}{100} = 1.2x \]

5. **Calculating Profit:**
- Profit is calculated as:
\[ \text{Profit} = SP - CP \]
- For 100 mangoes, the total selling price is:
\[ SP = 100y = 100 \times 1.2x = 120x \]
- The total cost price for 100 mangoes is:
\[ CP = 100x \]
- Therefore, the profit for 100 mangoes is:
\[ \text{Profit} = SP - CP = 120x - 100x = 20x \]

6. **Calculating Profit Percentage:**
- Profit percentage is given by the formula:
\[ \text{Profit Percent} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]
- Substituting the values we found:
\[ \text{Profit Percent} = \left(\frac{20x}{100x}\right) \times 100 = \left(\frac{20}{100}\right) \times 100 = 20\% \]

### Final Answer:
The profit percentage in this transaction is **20%**.