The marked price of a laptop is Rs. 12000. In a clearance sale it is sold at a discount of 15%, in - curring a loss of 4%. What is the cost price of the laptop ?

Options

A. Rs. 10200
B. Rs. 10625
C. Rs. 11200
D. Rs. 10275

Answer

To find the cost price of the laptop, we can follow these steps:

### Step 1: Calculate the Selling Price (SP)
The marked price (MP) of the laptop is Rs. 12,000. It is sold at a discount of 15%.

To calculate the discount amount:
\[ \text{Discount} = \text{Marked Price} \times \left(\frac{\text{Discount Percentage}}{100}\right) \]
\[ \text{Discount} = 12000 \times \left(\frac{15}{100}\right) = 12000 \times 0.15 = 1800 \]

Now, we can find the Selling Price (SP):
\[ \text{SP} = \text{Marked Price} - \text{Discount} \]
\[ \text{SP} = 12000 - 1800 = 10200 \]

### Step 2: Set up the equation for Cost Price (CP)
It is given that selling the laptop incurs a loss of 4%. This means that the Selling Price is 96% of the Cost Price.

We can express this relationship as:
\[ \text{SP} = \text{CP} - \text{Loss} \]
Since the loss is 4% of CP, we can rewrite it as:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{4}{100}\right) = \text{CP} \times \left(\frac{96}{100}\right) \]

### Step 3: Substitute the Selling Price into the equation
Now we can substitute the SP we calculated into the equation:
\[ 10200 = \text{CP} \times \left(\frac{96}{100}\right) \]

### Step 4: Solve for Cost Price (CP)
To find CP, we rearrange the equation:
\[ \text{CP} = 10200 \times \left(\frac{100}{96}\right) \]
Calculating this gives:
\[ \text{CP} = 10200 \times \frac{100}{96} = 10200 \times 1.04166667 \approx 10625 \]

Thus, the cost price of the laptop is Rs. 10,625.

### Summary
The cost price of the laptop is Rs. 10,625.

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