The marked price of an article is equal to (10/7) times its cost price, and the selling price is equal to (4/5) of the marked price. What is the profit percentage earned on the article?

Introduction / Context:
This question checks understanding of the relationship between cost price, marked price, and selling price. Instead of direct percentages, the problem describes these prices in terms of simple fractions, which must be converted into multiplication factors. The final goal is to compute the profit percentage based on the relationship between selling price and cost price, a fundamental concept in profit and loss problems.

Given Data / Assumptions:

• Cost price of the article = C.
• Marked price (MP) = (10/7) * C.
• Selling price (SP) = (4/5) * MP.
• We need to find the profit percentage based on C and SP.
• No discounts other than the given fraction of the marked price are applied.

Concept / Approach:
The central idea is to express selling price directly in terms of cost price. Once SP is expressed as a multiple of C, profit is SP − C. Dividing the profit by C and multiplying by 100 gives the profit percentage. Working with fractions is often easier than converting everything into decimals, and it avoids rounding errors. Here, we chain two factors: marked price over cost price and selling price over marked price to get selling price over cost price.

Step-by-Step Solution:
Let the cost price be C.Marked price MP = (10/7) * C.Selling price SP = (4/5) * MP = (4/5) * (10/7) * C.Compute SP: SP = (40/35) * C = (8/7) * C.Profit = SP − C = (8/7)C − C = (8/7 − 7/7)C = (1/7)C.Profit percentage = (Profit / C) * 100 = (1/7) * 100 ≈ 14.2857%.Rounded to two decimal places, profit percentage is 14.28%.

Verification / Alternative check:
Assume a convenient cost price, such as C = Rs. 7.Then MP = (10/7) * 7 = Rs. 10.SP = (4/5) * 10 = Rs. 8.Profit = 8 − 7 = Rs. 1.Profit percentage = (1 / 7) * 100 ≈ 14.2857%, confirming our result.

Why Other Options Are Wrong:
17.24% and 16.66% do not match the exact fractional profit of 1/7 of the cost price.15.42% is also not equal to (1/7) * 100 and comes from incorrect approximate calculations.Only 14.28% correctly represents the exact profit percentage.

Common Pitfalls:
A common mistake is to subtract the fractions 10/7 and 4/5 directly without properly chaining them as multipliers.Another error is to compute profit percentage using marked price instead of cost price as the base.Students sometimes round intermediate values too early, which slightly shifts the final percentage away from the correct option.

Final Answer:
The profit percentage earned on the article is 14.28% (approximately).