Question

The cost price 15 articles is equal to the selling price of 20 articles. Find the loss percentage.

• A. \(20\)\(\%\)
• B. \(30\)\(\%\)
• C. \(40\)\(\%\)
• D. \(25\)\(\%\)

Answer 1

The Correct Option is D

Let the cost price (CP) of 1 article be \(C\). Therefore, the cost price of 15 articles is \(15C\). Similarly, let the selling price (SP) of 1 article be \(S\). Therefore, the selling price of 20 articles is \(20S\). We are given that the cost price of 15 articles is equal to the selling price of 20 articles. So, we have:

\[15C = 20S\]

The cost price \(C\) can be expressed in terms of \(S\) as follows:

\[C = \frac{20S}{15} = \frac{4S}{3}\]

Here the cost price is more than the selling price, indicating a loss.

The loss per article can be calculated as:

\[\text{Loss} = C - S = \frac{4S}{3} - S = \frac{4S}{3} - \frac{3S}{3} = \frac{S}{3}\]

The loss percentage is given by:

\[\text{Loss Percentage} = \left(\frac{\text{Loss}}{C}\right) \times 100 = \left(\frac{\frac{S}{3}}{\frac{4S}{3}}\right) \times 100 = \left(\frac{S}{4S}\right) \times 100 = \frac{1}{4} \times 100 = 25\%\]

Therefore, the loss percentage is \(25\%\).