A person sells 320 mangoes at the cost of 400 mangoes. What is his profit per cent ?

Options

A. `10%`
B. `15%`
C. `20%`
D. `25%`

Answer

To find the profit percent when a person sells 320 mangoes at the cost of 400 mangoes, we can follow these steps:

### Step 1: Understand the Cost Price (CP) and Selling Price (SP)
Let the cost price of one mango be \( X \) rupees. Therefore, the cost price of 400 mangoes will be:
\[ \text{CP of 400 mangoes} = 400 \times X = 400X \text{ rupees} \]

### Step 2: Calculate the Selling Price (SP)
According to the problem, the selling price of 320 mangoes is equal to the cost price of 400 mangoes. Therefore:
\[ \text{SP of 320 mangoes} = 400X \text{ rupees} \]

### Step 3: Calculate the Cost Price of 320 Mangoes
The cost price of 320 mangoes is:
\[ \text{CP of 320 mangoes} = 320 \times X = 320X \text{ rupees} \]

### Step 4: Calculate the Profit
Profit can be calculated using the formula:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Substituting the values we have:
\[ \text{Profit} = 400X - 320X = 80X \text{ rupees} \]

### Step 5: Calculate the Profit Percent
Profit percent is calculated using the formula:
\[ \text{Profit Percent} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percent} = \left( \frac{80X}{320X} \right) \times 100 \]
The \( X \) cancels out:
\[ \text{Profit Percent} = \left( \frac{80}{320} \right) \times 100 \]
Simplifying \( \frac{80}{320} \):
\[ \frac{80}{320} = \frac{1}{4} \]
So,
\[ \text{Profit Percent} = \left( \frac{1}{4} \right) \times 100 = 25\% \]

### Final Answer
The profit percent is **25%**.