What profit/loss percent did ravi earn, if he purchased an item of 5600 and sold it at three fourth of its cost price?

Options

A. loss of 20%
B. Gain of 25%
C. neither gain nor loss
D. None of these

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the Cost Price (CP)
The cost price of the item is given as:
\[ \text{CP} = 5600 \text{ Rs} \]

### Step 2: Calculate the Selling Price (SP)
The selling price is given as three-fourths of the cost price. We can calculate it as follows:
\[ \text{SP} = \frac{3}{4} \times \text{CP} = \frac{3}{4} \times 5600 \]
Calculating this gives:
\[ \text{SP} = \frac{3 \times 5600}{4} = \frac{16800}{4} = 4200 \text{ Rs} \]

### Step 3: Determine the Loss
To find the loss, we subtract the selling price from the cost price:
\[ \text{Loss} = \text{CP} - \text{SP} = 5600 - 4200 = 1400 \text{ Rs} \]

### Step 4: Calculate the Loss Percentage
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{CP}}\right) \times 100 \]
Substituting the values we have:
\[ \text{Loss Percentage} = \left(\frac{1400}{5600}\right) \times 100 \]

### Step 5: Simplify the Loss Percentage Calculation
Now we simplify:
\[ \text{Loss Percentage} = \left(\frac{1400 \div 1400}{5600 \div 1400}\right) \times 100 = \left(\frac{1}{4}\right) \times 100 = 25\% \]

### Final Answer
Ravi incurred a loss of **25%**.

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