Difficulty: Easy
Correct Answer: 25%
Explanation:
Introduction / Context:
This is a classic profit and loss problem where an equality between the cost of several items and the selling price of fewer items is given. From this, we infer the relationship between cost price and selling price of a single item and compute the profit percentage. It is widely used in exams to test understanding of ratios and percentages without needing explicit rupee values.
Given Data / Assumptions:
Concept / Approach:
From the equality 25C = 20S, we can find the ratio S : C. Once S is expressed as a multiple of C, we can compute the profit per book as S − C. Profit percentage is then (S − C)/C * 100. Because only the ratio matters, C and S themselves need not be known; their ratio captures the entire profit behavior.
Step-by-Step Solution:
Given: 25C = 20S.Rearrange to find S/C: divide both sides by 5 ⇒ 5C = 4S.So S = (5/4) * C.Profit per book = S − C = (5/4)C − C = (1/4)C.Profit percentage = (Profit / C) * 100 = (1/4) * 100 = 25%.Thus, the profit percentage on each book is 25%.
Verification / Alternative check:
Assume C = Rs. 4 per book.Then S = (5/4) * 4 = Rs. 5 per book.Cost of 25 books = 25 * 4 = Rs. 100.Selling price of 20 books = 20 * 5 = Rs. 100.This matches the given condition, confirming the ratio is correct.Profit per book = 5 − 4 = Rs. 1, which is 25% of the cost price.
Why Other Options Are Wrong:
20%, 22%, and 24% would correspond to different S : C ratios and would not satisfy the equation 25C = 20S.Only a profit of 25% produces the precise relationship stated in the problem.
Common Pitfalls:
Some learners mistakenly treat 25 and 20 as the number of books sold at different times, instead of using them to connect CP and SP.Another pitfall is misreading the equality and forming 20C = 25S, which completely changes the ratio.A few students divide incorrectly and calculate S/C improperly, leading to wrong profit percentages.
Final Answer:
The profit percentage earned on each book is 25%.
Discussion & Comments