The selling price of an article is eight fifths of its cost price. What is the percentage gain made on this article?

Introduction / Context:
This is a direct profit percentage calculation based on a given ratio of selling price to cost price. Problems of this type are frequently asked to test whether the candidate can quickly convert a ratio into a profit percentage.

Given Data / Assumptions:

• Selling price (SP) is 8/5 of cost price (CP).
• We need to calculate the profit percentage.
• Cost price and selling price are positive real values.

Concept / Approach:
Profit is defined as SP minus CP. Profit percentage is given by (profit / CP) * 100. With SP expressed as a multiple of CP, the algebra becomes simple. To avoid dealing with fractions later, we can assume a convenient value for CP that clears the denominator.

Step-by-Step Solution:
Let cost price CP = 5 units (to match denominator of 5).Then selling price SP = (8/5) * CP = (8/5) * 5 = 8 units.Profit = SP - CP = 8 - 5 = 3 units.Profit percentage = (profit / CP) * 100 = (3 / 5) * 100.So profit percentage = 60 percent.

Verification / Alternative check:
We can also use a different cost price, for example CP = 10. Then SP = (8/5) * 10 = 16, profit = 6 and profit percentage = 6 / 10 * 100 = 60 percent. This confirms that the result is independent of the particular cost price chosen.

Why Other Options Are Wrong:
Profit percentages 20 percent, 28 percent and 68 percent do not match the ratio 8/5. They would correspond to different SP to CP ratios. Only 60 percent correctly reflects that the selling price is 1.6 times the cost price, yielding a 0.6 CP profit.

Common Pitfalls:
Candidates sometimes confuse the ratio and directly treat 8/5 as 8 percent or 5 percent, which is wrong. Another common error is to compute (SP / CP) * 100 instead of (SP - CP) / CP * 100, which gives 160 percent, not the profit percentage. Always apply the correct profit formula.

Final Answer:
The gain percentage on the article is 60 percent.