If an article is sold at a loss of 20%, by what fraction must the selling price be multiplied to obtain the cost price of the article?

Introduction / Context:
This question checks basic understanding of how cost price, selling price, and loss percentage are related. Instead of asking for the percentage directly, it asks for the fraction that converts the selling price back into the cost price when there is a known percentage loss. Such conceptual questions are common in quantitative aptitude sections to ensure students understand percentages as multipliers.

Given Data / Assumptions:

• Loss percentage on the article is 20%.
• We denote cost price by CP and selling price by SP.
• Loss percent is defined on cost price.
• We need a fraction k such that CP = k * SP.

Concept / Approach:
Use the standard relationships:

• Loss percent = ((CP - SP) / CP) * 100.
• 20% loss means SP = 80% of CP.
• So SP = 0.8 * CP which is also 4/5 of CP.
• We need CP in terms of SP, so invert the relationship.
• Thus CP = SP / 0.8 = SP * (5/4).

Therefore, the required multiplying fraction is 5/4.

Step-by-Step Solution:
Let cost price be CP. Loss percent is 20%, so loss = 20% of CP. Therefore SP = CP - 20% of CP. SP = CP - 0.2CP = 0.8CP. Thus SP = (4/5) * CP. We want CP in terms of SP, so CP = SP / (4/5). CP = SP * (5/4). Hence, the selling price must be multiplied by 5/4 to get the cost price.

Verification / Alternative check:
Assume an easy cost price, for example CP = 100 rupees. A 20% loss means loss = 20 rupees, so SP = 80 rupees. Now, multiply SP by 5/4:

• SP * (5/4) = 80 * (5/4) = 80 * 1.25 = 100.

We get back the original cost price. This confirms that 5/4 is the correct fraction. Any other fraction will not return the cost price from the selling price when the loss is 20%.

Why Other Options Are Wrong:
4/5 would reduce the selling price further and cannot give the higher cost price. 8/5 and 6/5 are too large or not consistent with the 20% loss relation. 3/2 equals 1.5 and would correspond to a different percentage relationship. Only 5/4 correctly inverts the 20% loss scenario where SP is 80% of CP.

Common Pitfalls:
Many learners confuse whether to multiply by (100 - loss%) or divide by it. Some directly assume CP = SP * 0.8, which is the reverse of the correct relation. Always remember: if SP is 80% of CP, then CP must be larger and is obtained by dividing SP by 0.8 or multiplying by 5/4.

Final Answer:
The selling price must be multiplied by the fraction 5/4 to get the cost price.