Lavanya lost 20% by selling a mobile for Rs.3072. What per cent will she gain by it for Rs.4080?

Options

A. 0.06
B. `5.25%`
C. `6.25%`
D. `6.75%`

Answer

To solve the problem step by step, we will follow the method outlined in the video transcript.

### Step 1: Identify the Selling Price and Loss Percentage
Lavanya sold the mobile for Rs. 3072 and incurred a loss of 20%.

### Step 2: Calculate the Cost Price (CP)
To find the cost price when we know the selling price and the loss percentage, we can use the formula:

\[ \text{Cost Price (CP)} = \frac{\text{Selling Price (SP)} \times 100}{100 - \text{Loss Percentage}} \]

Substituting the values we have:

\[ \text{CP} = \frac{3072 \times 100}{100 - 20} = \frac{3072 \times 100}{80} \]

### Step 3: Simplify the Calculation
Now, we simplify the calculation:

\[ \text{CP} = \frac{307200}{80} = 3840 \]

So, the cost price of the mobile is Rs. 3840.

### Step 4: Calculate the New Selling Price
Now, we want to find out the profit percentage if Lavanya sells the mobile for Rs. 4080.

### Step 5: Calculate the Profit
Profit can be calculated as:

\[ \text{Profit} = \text{New Selling Price} - \text{Cost Price} \]

Substituting the values:

\[ \text{Profit} = 4080 - 3840 = 240 \]

### Step 6: Calculate the Profit Percentage
The profit percentage can be calculated using the formula:

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

Substituting the values:

\[ \text{Profit Percentage} = \left(\frac{240}{3840} \times 100\right) \]

### Step 7: Simplify the Profit Percentage Calculation
Now, simplifying the calculation:

\[ \text{Profit Percentage} = \left(\frac{240 \times 100}{3840}\right) = \frac{24000}{3840} \]

Now, dividing:

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

### Conclusion
The percentage gain when Lavanya sells the mobile for Rs. 4080 is **6.25%**.

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