ITC sells one product at a profit of 20% another at a loss of 20% at the same selling price. If SP of each article be Rs. 200, what is the amount of loss?

Options

A. A. Rs. 10
B. B. Rs. 16
C. C. Rs. 16.66
D. D. none of these

Answer

To solve the problem step by step, we need to find the amount of loss incurred by ITC when selling two products at the same selling price of Rs. 200, one at a profit of 20% and the other at a loss of 20%.

### Step 1: Calculate the Cost Price of the Product Sold at a Profit of 20%
To find the cost price (CP) when selling at a profit, we use the formula:
\[ CP = \frac{SP}{1 + \frac{P}{100}} \]
Where:
- SP = Selling Price = Rs. 200
- P = Profit Percentage = 20%

Substituting the values:
\[ CP_{profit} = \frac{200}{1 + \frac{20}{100}} = \frac{200}{1.2} = \frac{200}{1.2} = 166.67 \text{ (approximately)} \]

### Step 2: Calculate the Cost Price of the Product Sold at a Loss of 20%
To find the cost price when selling at a loss, we use the formula:
\[ CP = \frac{SP}{1 - \frac{L}{100}} \]
Where:
- SP = Selling Price = Rs. 200
- L = Loss Percentage = 20%

Substituting the values:
\[ CP_{loss} = \frac{200}{1 - \frac{20}{100}} = \frac{200}{0.8} = 250 \]

### Step 3: Calculate the Total Cost Price
Now, we can find the total cost price by adding the cost prices of both products:
\[ Total \, CP = CP_{profit} + CP_{loss} = 166.67 + 250 = 416.67 \text{ (approximately)} \]

### Step 4: Calculate the Total Selling Price
Since both products are sold at the same selling price:
\[ Total \, SP = SP_{profit} + SP_{loss} = 200 + 200 = 400 \]

### Step 5: Calculate the Amount of Loss
Now, we can find the amount of loss by subtracting the total selling price from the total cost price:
\[ Loss = Total \, CP - Total \, SP = 416.67 - 400 = 16.67 \text{ (approximately)} \]

### Final Answer
The amount of loss incurred by ITC is approximately Rs. 16.67.

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