12 copies of a book were sold for Rs.1800 thereby gaining cost price of 3 copies.The cost price of a copy of the book is :

Options

A. Rs.120
B. Rs.150
C. Rs.1200
D. Rs.1500

Answer

To find the cost price of a copy of the book, we can follow these steps:

### Step 1: Understand the Selling Price and Profit
We know that 12 copies of the book were sold for Rs. 1800. The profit made from selling these 12 copies is equivalent to the cost price of 3 copies.

### Step 2: Set Up the Equation
Let the cost price of one copy of the book be \( CP \). Therefore, the total cost price of 12 copies is:
\[ Total\ CP = 12 \times CP \]
The profit from selling 12 copies is the cost price of 3 copies, which can be expressed as:
\[ Profit = 3 \times CP \]

### Step 3: Relate Selling Price, Cost Price, and Profit
Using the formula for selling price:
\[ Selling\ Price = Cost\ Price + Profit \]
We can substitute the known values:
\[ 1800 = (12 \times CP) + (3 \times CP) \]

### Step 4: Combine Like Terms
Combine the terms on the right side:
\[ 1800 = 15 \times CP \]

### Step 5: Solve for Cost Price
Now, we can solve for \( CP \):
\[ CP = \frac{1800}{15} \]
Calculating this gives:
\[ CP = 120 \]

### Conclusion
The cost price of one copy of the book is Rs. 120.

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