Two mobile phones are sold at Rs.6000 each. The first mobile is sold at 20 % profit and the other one at 25 % loss. What is the percentage of loss or profit incurred during the deal ?

Options

A. 7.7% loss
B. 8.3 % loss
C. 9% loss
D. 2 % profit

Answer

To solve the problem step by step, we need to find the cost price of each mobile phone, calculate the total cost price, and then compare it with the total selling price to determine the overall profit or loss.

### Step 1: Calculate the Cost Price of the First Mobile Phone
The first mobile is sold at a 20% profit. Let the cost price of the first mobile be \( CP_1 \).

The selling price (SP) is given as Rs. 6000. We can use the formula for profit:

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

Where Profit = 20% of \( CP_1 \):

\[ 6000 = CP_1 + 0.20 \times CP_1 \]

This simplifies to:

\[ 6000 = CP_1 (1 + 0.20) = CP_1 \times 1.20 \]

Now, we can solve for \( CP_1 \):

\[ CP_1 = \frac{6000}{1.20} = 5000 \]

### Step 2: Calculate the Cost Price of the Second Mobile Phone
The second mobile is sold at a 25% loss. Let the cost price of the second mobile be \( CP_2 \).

The selling price is again Rs. 6000. We can use the formula for loss:

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

Where Loss = 25% of \( CP_2 \):

\[ 6000 = CP_2 - 0.25 \times CP_2 \]

This simplifies to:

\[ 6000 = CP_2 (1 - 0.25) = CP_2 \times 0.75 \]

Now, we can solve for \( CP_2 \):

\[ CP_2 = \frac{6000}{0.75} = 8000 \]

### Step 3: Calculate Total Cost Price
Now we can find the total cost price of both mobile phones:

\[ \text{Total Cost Price} = CP_1 + CP_2 = 5000 + 8000 = 13000 \]

### Step 4: Calculate Total Selling Price
The total selling price of both mobile phones is:

\[ \text{Total Selling Price} = 6000 + 6000 = 12000 \]

### Step 5: Calculate Overall Profit or Loss
Now we can find the overall profit or loss:

\[ \text{Loss} = \text{Total Cost Price} - \text{Total Selling Price} = 13000 - 12000 = 1000 \]

### Step 6: Calculate the Percentage of Loss
To find the percentage of loss, we use the formula:

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

Substituting the values:

\[ \text{Percentage of Loss} = \left( \frac{1000}{13000} \right) \times 100 \approx 7.69\% \]

### Conclusion
The overall loss incurred during the deal is approximately **7.69%**.

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