By selling a cell phone for र2400 ,a shopkeeper make a profit of 25%.Then,his profit percentage, if he had sold it for र 2040, is

Options

A. `10%`
B. `6.25%`
C. `6.5%`
D. `15%`

Answer

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

### Step 1: Determine the Cost Price (CP) of the cell phone
Given that the Selling Price (SP) is र2400 and the profit percentage is 25%, we can use the formula for selling price:

\[ SP = CP + \text{Profit} \]

Since profit is 25% of the cost price (CP), we can express this as:

\[ SP = CP + 0.25 \times CP = 1.25 \times CP \]

Rearranging the formula to find CP, we have:

\[ CP = \frac{SP}{1.25} \]

Substituting the given SP:

\[ CP = \frac{2400}{1.25} \]

### Step 2: Calculate CP
To simplify the division, we can multiply the numerator and denominator by 100:

\[ CP = \frac{2400 \times 100}{125} = \frac{240000}{125} \]

Now, we perform the division:

\[ CP = 1920 \]

### Step 3: Calculate Profit when sold for र2040
Now, we need to find the profit if the cell phone is sold for र2040. The profit can be calculated as:

\[ \text{Profit} = SP - CP \]

Substituting the values:

\[ \text{Profit} = 2040 - 1920 = 120 \]

### Step 4: Calculate Profit Percentage
The profit percentage is calculated using the formula:

\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]

Substituting the values we have:

\[ \text{Profit Percentage} = \left(\frac{120}{1920}\right) \times 100 \]

### Step 5: Simplify the Profit Percentage Calculation
Calculating the fraction:

\[ \text{Profit Percentage} = \frac{120 \times 100}{1920} \]

This simplifies to:

\[ \text{Profit Percentage} = \frac{12000}{1920} \]

Now, we can simplify this fraction:

1. Dividing both the numerator and denominator by 240:

\[ \text{Profit Percentage} = \frac{50}{8} = 6.25 \]

Thus, the profit percentage is:

\[ \text{Profit Percentage} = 6.25\% \]

### Final Answer
The profit percentage if the shopkeeper sold the cell phone for र2040 is **6.25%**.

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