Raju sold an item for Rs 6,000/- at a loss of 25%. At what cost would he have purchased that item?

Options

A. Rs 7500
B. Rs. 7200
C. Rs. 8000
D. Rs. 8500

Answer

To find the cost price of the item that Raju sold for Rs. 6,000 at a loss of 25%, we can follow these steps:

### Step 1: Understand the relationship between cost price, selling price, and loss percentage.
Let the cost price (CP) of the item be denoted as \( X \). A loss of 25% means that Raju sold the item for 75% of its cost price (since 100% - 25% = 75%).

### Step 2: Write the equation for the selling price.
The selling price (SP) can be expressed as:
\[ SP = CP - \text{Loss} \]
Since the loss is 25% of the cost price, we can also express it as:
\[ SP = CP - 0.25 \times CP = 0.75 \times CP \]
Thus, we can write:
\[ SP = 0.75X \]

### Step 3: Substitute the selling price into the equation.
We know that Raju sold the item for Rs. 6,000, so we can set up the equation:
\[ 0.75X = 6000 \]

### Step 4: Solve for the cost price (X).
To find \( X \), we can rearrange the equation:
\[ X = \frac{6000}{0.75} \]

### Step 5: Calculate the value of X.
Now, performing the division:
\[ X = 6000 \div 0.75 = 6000 \times \frac{100}{75} = 6000 \times \frac{4}{3} = 8000 \]

### Conclusion:
The cost price of the item is Rs. 8,000.