Ramesh sold a book at a loss of 30%. If he had sold it for Rs. 140 more, he would have made a profit of 40%. The cost price of the book is

Options

A. a)Rs 280
B. b)Rs 200
C. c)Rs 260
D. d)Rs 300

Answer

To find the cost price (CP) of the book that Ramesh sold, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Selling Prices**:
- Ramesh sold the book at a loss of 30%. Therefore, the selling price (SP1) can be expressed as:
\[ SP1 = CP - (30\% \text{ of } CP) = CP \times \left(1 - \frac{30}{100}\right) = CP \times 0.7 \]

2. **Calculate the Selling Price for Profit**:
- If Ramesh had sold the book for Rs. 140 more, he would have made a profit of 40%. Therefore, the new selling price (SP2) can be expressed as:
\[ SP2 = CP + (40\% \text{ of } CP) = CP \times \left(1 + \frac{40}{100}\right) = CP \times 1.4 \]

3. **Set Up the Equation**:
- According to the problem, the difference between the two selling prices (SP2 - SP1) is Rs. 140:
\[ SP2 - SP1 = 140 \]
- Substituting the expressions for SP1 and SP2:
\[ (CP \times 1.4) - (CP \times 0.7) = 140 \]

4. **Simplify the Equation**:
- Combine like terms:
\[ CP \times (1.4 - 0.7) = 140 \]
- This simplifies to:
\[ CP \times 0.7 = 140 \]

5. **Solve for Cost Price (CP)**:
- To find CP, divide both sides by 0.7:
\[ CP = \frac{140}{0.7} \]
- Calculating this gives:
\[ CP = 200 \]

### Final Answer:
The cost price of the book is Rs. 200.