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 solve the problem step by step, let's break it down:

### Step 1: Understand the given information
We know that:
- Selling Price (SP) of 12 copies = Rs. 1800
- Profit is equal to the cost price (CP) of 3 copies.

### Step 2: Set up the equations
Let the cost price of one copy be \( CP \).
Then, the total cost price of 12 copies = \( 12 \times CP \).

According to the problem, the profit from selling 12 copies is equal to the cost price of 3 copies:
\[ \text{Profit} = CP \times 3 \]

### Step 3: Relate Selling Price, Cost Price, and Profit
We know that:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
So, we can write:
\[ 1800 = 12 \times CP + 3 \times CP \]
This simplifies to:
\[ 1800 = 15 \times CP \]

### Step 4: Solve for the Cost Price of one copy
Now, we can find \( CP \):
\[ CP = \frac{1800}{15} \]

### Step 5: Calculate the value
Calculating this gives:
\[ CP = 120 \]

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

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