The profit on selling 35 mangoes is equal to the cost price of 7 mangoes. What is the profit percentage?

Options

A. `33(1)/(3)`
B. `20`
C. `25`
D. `16(2)/(3)`

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the relationship between profit and cost price
According to the question, the profit from selling 35 mangoes is equal to the cost price of 7 mangoes.

### Step 2: Let’s define variables
Let the cost price of one mango be \( CP \).
Then, the cost price of 7 mangoes is \( 7 \times CP \).

### Step 3: Calculate the profit
The profit from selling 35 mangoes is equal to the cost price of 7 mangoes:
\[ \text{Profit} = 7 \times CP \]

### Step 4: Calculate the cost price of 35 mangoes
The cost price of 35 mangoes is:
\[ \text{Cost Price of 35 mangoes} = 35 \times CP \]

### Step 5: Set up the profit equation
The profit can also be expressed as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
Let \( SP \) be the selling price of 35 mangoes. Then:
\[ \text{Profit} = SP - (35 \times CP) \]
Since we know that the profit is also \( 7 \times CP \), we can set up the equation:
\[ SP - (35 \times CP) = 7 \times CP \]

### Step 6: Solve for Selling Price
Rearranging the equation gives:
\[ SP = 35 \times CP + 7 \times CP \]
\[ SP = 42 \times CP \]

### Step 7: Calculate the profit percentage
Profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit} = 7 \times CP \]
\[ \text{Cost Price} = 35 \times CP \]
Thus,
\[ \text{Profit Percentage} = \left( \frac{7 \times CP}{35 \times CP} \right) \times 100 \]
The \( CP \) cancels out:
\[ \text{Profit Percentage} = \left( \frac{7}{35} \right) \times 100 \]
\[ \text{Profit Percentage} = \left( \frac{1}{5} \right) \times 100 = 20\% \]

### Final Answer
The profit percentage is **20%**.

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