Question

If selling price of 80 articles is equal to the cost price of 100 articles, then find the gain percentage.

• A. \( 30 \)
• B. \( 25 \)
• C. \( 40 \)
• D. \( 50 \)

Hint:

\textbf{Profit and Loss with Articles.} When the selling price of a certain number of articles is equal to the cost price of another number of articles, you can easily calculate the gain or loss percentage by considering the relationship between the total SP and total CP. If \(SP\) of \(m\) articles \( = CP\) of \(n\) articles, then \( \text{Gain/Loss} = \frac{n-m}{m} \times 100 \). In this case, \( \frac{100-80}{80} \times 100 = \frac{20}{80} \times 100 = 25 \).

Answer 1

The Correct Option is B

Let the selling price of one article be \(SP\) and the cost price of one article be \(CP\). According to the problem, the selling price of 80 articles is equal to the cost price of 100 articles. So, \(80 \times SP = 100 \times CP\) We can find the ratio of selling price to cost price: $$ \frac{SP}{CP} = \frac{100}{80} = \frac{5}{4} $$ This means that for every 4 units of cost price, the selling price is 5 units. Gain \( = SP - CP \) Let's consider the cost price of 4 articles as \(4x\). Then the selling price of 4 articles would be \(5x\). Gain \( = 5x - 4x = x \) Gain percentage is calculated as: $$ \text{Gain Percentage} = \frac{\text{Gain}}{\text{Cost Price}} \times 100 $$ $$ \text{Gain Percentage} = \frac{x}{4x} \times 100 $$ $$ \text{Gain Percentage} = \frac{1}{4} \times 100 $$ $$ \text{Gain Percentage} = 25 $$ Therefore, the gain percentage is 25%.