Question

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? (a) \(1 \%\) (b) \(2 \%\) (c) \(4 \%\) (d) \(0 \%\)

Short answer

Answer: (c) 4%

Step-by-step solution

Calculate the profit and loss in terms of cost price

Let the cost price of the first product be \(x\) and that of the second product be \(y\). Since the selling price is the same for both, we can create two equations to represent the profit and loss calculations: Product 1: Profit = \(20\%\) of cost price, so Selling price = \(1 + 0.20 = 1.20x\). Product 2: Loss = \(20\%\) of cost price, so Selling price = \(1 - 0.20 = 0.80y\).

Equate the selling prices

Since both products have the same selling price, we can equate the two selling price expressions: \(1.20x = 0.80y\).

Solve for the ratio of cost prices

To solve for the ratio \(\frac{x}{y}\), divide both sides of the equation by \(0.80\) on the left side and by \(1.20\) on the right side: \(\frac{x}{y} = \frac{0.80}{1.20}\). Now simplify this fraction: \(\frac{x}{y} = \frac{4}{6} = \frac{2}{3}\).

Calculate the overall percentage change

To find how much loss is incurred by ITC, we will calculate the effective percentage change in cost price. Let's assume both products have the same cost price of \(100\). Therefore, the cost price of the first product is \(2x = 200\) and the second product is \(3y = 300\). The total cost price is \(500\). The selling price of product 1 = \(1.20(200) = 240\) The selling price of product 2 = \(0.80(300) = 240\) The total selling price = \(480\) Now find the percentage loss: Percentage loss \(\% = \frac{(Total\;cost\;price - Total\;selling\;price)}{Total\;cost\;price} \times100\) Percentage loss \(\% = \frac{(500-480)}{500} \times100\)

Calculate the percentage loss and find the correct answer

Now, calculate the percentage loss: Percentage loss \(\% = \frac{20}{500} \times100 = 4 \%\) The answer is (c) \(4 \%\).

Key concepts

Cost Price

The cost price is essentially the amount paid to acquire a product before selling it. It's the original price of the item before any profit or loss adjustments.

• In the scenario of ITC, let's assume each product has its separate cost price, denoted by variables such as \(x\) for the first product and \(y\) for the second product.
• Understanding the cost price helps us calculate both profit and loss because it serves as the base figure for these calculations.

A higher cost price means less room for profit if selling prices remain constant. Therefore knowing the cost price is fundamental when analyzing financial outcomes, especially in business contexts.

Selling Price

The selling price is what an item is sold for. It's the final price that is decided upon after considering the profit margin or loss to ensure a successful sale.

• In the given problem, both products are sold at the same selling price, showing different financial outcomes—one at a profit and the other at a loss.
• Using the cost price, the selling price of the first product becomes \(1.20x\), representing a profit, whereas the second product's selling price of \(0.80y\) indicates a loss.

Understanding how to set the right selling price is crucial for financial strategies, as it directly impacts the total revenue and overall business success.

Percentage Loss

Percentage loss refers to the decrease in value from the cost price and is expressed as a percentage of the original cost price. It's calculated when the selling price is less than the cost price.

• In the example, the total cost price is higher than the total selling price, indicating a loss.
• The formula to find percentage loss is: \[\text{Percentage Loss} \% = \frac{\text{(Total Cost Price - Total Selling Price)}}{\text{Total Cost Price}} \times 100\]

Here, ITC's total cost was \(500\) and the total selling price was \(480\), leading to a loss percentage of \(4\%\). Calculating this helps businesses understand financial losses to adjust strategies accordingly.

Profit Percentage

Profit percentage is achieved when the selling price exceeds the cost price. Like percentage loss, but in reverse, it's expressed as a percentage of the cost price.

• In this scenario, for the first product, the selling price was \(1.20x\), meaning there was a \(20\%\) profit based on its individual cost price \(x\).
• The formula for profit percentage is:\[\text{Profit Percentage} \% = \frac{\text{(Selling Price - Cost Price)}}{\text{Cost Price}} \times 100\]

A higher profit percentage represents a better financial position for a business, and knowing how to calculate this allows businesses to maximize their strategies.