Twelve copies of a book are sold for Rs. 1,800, and in doing so the seller gains an amount equal to the cost price of three copies. What is the cost price of one copy of the book?

Introduction / Context:
This profit and loss problem describes a situation where the total profit from selling a set of books is equal to the cost of a smaller number of those books. From this information, we are asked to find the cost price of a single copy. The language is typical of exam problems that require converting verbal profit conditions into clear algebraic equations.

Given Data / Assumptions:

• Number of books sold = 12.
• Total selling price of 12 books = Rs. 1,800.
• Let the cost price of 1 book be C.
• Total cost price of 12 books = 12C.
• Total profit is equal to the cost price of 3 books, which is 3C.
• We assume all books are identical and sold at the same selling price per copy.

Concept / Approach:
The total profit from selling all 12 books is the difference between total selling price and total cost price. According to the question, this profit equals the cost of 3 books. Thus, (Total selling price − Total cost price) = 3C. Using this relationship, we can form an equation in C and solve for the cost price per book. Once C is known, it can be matched to the given options.

Step-by-Step Solution:
Let cost price of one book be C.Total cost price of 12 books = 12C.Total selling price of 12 books = Rs. 1,800.Total profit = total selling price − total cost price = 1800 − 12C.Given that this total profit equals cost price of 3 books, so 1800 − 12C = 3C.Rearrange: 1800 = 12C + 3C = 15C.Thus, C = 1800 / 15 = Rs. 120.Therefore, the cost price of one copy of the book is Rs. 120.

Verification / Alternative check:
If each book costs Rs. 120, the total cost of 12 books is 12 * 120 = Rs. 1,440.Total selling price is Rs. 1,800, so profit = 1800 − 1440 = Rs. 360.Cost price of 3 books at Rs. 120 each is 3 * 120 = Rs. 360.Thus, the calculated cost price satisfies the condition that profit equals cost price of 3 books.

Why Other Options Are Wrong:
If C = Rs. 150, then total cost would be 12 * 150 = 1,800, leaving zero profit, which contradicts the condition.Rs. 1,200 and Rs. 1,500 as cost per book are far too large and would make the total cost many times the selling price.Only Rs. 120 gives a realistic and correct solution consistent with the problem statement.

Common Pitfalls:
A common mistake is to misinterpret “gaining cost price of 3 copies” as selling 3 extra books rather than profit equal to 3C.Students sometimes treat 1,800 as the profit instead of total selling price.Another pitfall is forgetting to multiply the cost price by 12 when computing total cost.

Final Answer:
The cost price of one copy of the book is Rs. 120.