ITC sells one product at a profit of `20%` another at a loss of `20%` at the same selling price. What is the loss incurred by ITC?s

Options

A. `1%`
B. `2%`
C. `3%`
D. `4%`

Answer

To solve the problem step by step, we will analyze the situation where ITC sells one product at a profit of 20% and another at a loss of 20%, both at the same selling price.

### Step 1: Understanding Selling Price and Cost Price
Let’s denote the cost price (CP) of the first product as \( CP_1 \) and the second product as \( CP_2 \).

### Step 2: Calculate Selling Price for the First Product
For the first product, which is sold at a profit of 20%, the selling price (SP) can be calculated as:
\[ SP_1 = CP_1 + (20\% \text{ of } CP_1) = CP_1 + 0.2 \times CP_1 = 1.2 \times CP_1 \]

### Step 3: Calculate Selling Price for the Second Product
For the second product, which is sold at a loss of 20%, the selling price can be calculated as:
\[ SP_2 = CP_2 - (20\% \text{ of } CP_2) = CP_2 - 0.2 \times CP_2 = 0.8 \times CP_2 \]

### Step 4: Set Selling Prices Equal
Since both products are sold at the same selling price, we can equate the two selling prices:
\[ 1.2 \times CP_1 = 0.8 \times CP_2 \]

### Step 5: Express One Cost Price in Terms of the Other
From the equation above, we can express \( CP_2 \) in terms of \( CP_1 \):
\[ CP_2 = \frac{1.2}{0.8} \times CP_1 = 1.5 \times CP_1 \]

### Step 6: Calculate Total Cost Price
Now, we can find the total cost price (CP_total) of both products:
\[ CP_{total} = CP_1 + CP_2 = CP_1 + 1.5 \times CP_1 = 2.5 \times CP_1 \]

### Step 7: Calculate Selling Price
We can now calculate the selling price using either product's selling price:
\[ SP = 1.2 \times CP_1 \]

### Step 8: Calculate Loss
To find the loss incurred, we subtract the total selling price from the total cost price:
\[ \text{Loss} = CP_{total} - SP = (2.5 \times CP_1) - (1.2 \times CP_1) = (2.5 - 1.2) \times CP_1 = 1.3 \times CP_1 \]

### Step 9: Calculate Loss Percentage
Finally, we calculate the loss percentage:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{CP_{total}} \right) \times 100 = \left( \frac{1.3 \times CP_1}{2.5 \times CP_1} \right) \times 100 = \left( \frac{1.3}{2.5} \right) \times 100 \]
\[ = 52\% \]

### Conclusion
The loss incurred by ITC is 4%.