The marked price of an item is Rs 5,800. If Ravi earns a profit of 25% after allowing a discount of 20%, then the cost price of the item is :

Options

A. Rs 3, 625
B. Rs 3,724
C. Rs 3,720
D. Rs 3,712

Answer

To find the cost price of the item, we will follow these steps:

### Step 1: Calculate the Selling Price (SP)
The marked price (MP) of the item is Rs 5,800. Ravi gives a discount of 20% on this marked price.

\[ \text{Discount} = \text{MP} \times \frac{20}{100} = 5800 \times 0.20 = 1160 \]

Now, we can find the selling price (SP):

\[ \text{SP} = \text{MP} - \text{Discount} = 5800 - 1160 = 4640 \]

### Step 2: Relate Selling Price to Cost Price
Ravi earns a profit of 25%. This means the selling price is 125% of the cost price (CP). We can express this relationship mathematically:

\[ \text{SP} = \text{CP} \times \frac{125}{100} = \text{CP} \times 1.25 \]

### Step 3: Solve for Cost Price
Now we can substitute the selling price we calculated into this equation:

\[ 4640 = \text{CP} \times 1.25 \]

To find the cost price (CP), we rearrange the equation:

\[ \text{CP} = \frac{4640}{1.25} \]

Calculating this gives:

\[ \text{CP} = 4640 \div 1.25 = 3712 \]

### Step 4: Final Answer
Thus, the cost price of the item is Rs 3,712.

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