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

Answer

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

### Step 1: Define Variables
Let the cost price of one copy of the book be Rs. K.

### Step 2: Calculate the Cost Price of 12 Copies
The cost price of 12 copies of the book will be:
\[ \text{Cost Price of 12 copies} = 12 \times K = 12K \]

### Step 3: Calculate the Profit
According to the problem, the profit gained from selling 12 copies is equal to the cost price of 3 copies. Therefore, the profit can be calculated as:
\[ \text{Profit} = \text{Cost Price of 3 copies} = 3 \times K = 3K \]

### Step 4: Calculate the Selling Price
The selling price (SP) can be calculated using the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Substituting the values we have:
\[ \text{SP} = 12K + 3K = 15K \]

### Step 5: Set the Selling Price Equal to the Given Value
From the problem, we know that the selling price of 12 copies is Rs. 1800:
\[ 15K = 1800 \]

### Step 6: Solve for K
To find the value of K, divide both sides by 15:
\[ K = \frac{1800}{15} = 120 \]

### Step 7: Conclusion
The cost price of one copy of the book is Rs. 120.

### Final Answer
The cost price of a copy of the book is Rs. 120.

---