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

Introduction / Context:
This problem is a standard profit and loss question where two different selling prices lead to two different percentages, one loss and one profit, on the same article. The difference between these selling prices is given, and we are asked to find the cost price. This type of question tests understanding of percentage profit and loss and the ability to set up a linear equation based on them.

Given Data / Assumptions:

• Ramesh sells the book at a loss of 30%.
• If he increases the selling price by Rs 140, he earns a profit of 40%.
• The cost price is the same in both scenarios.
• We need to find the cost price of the book.

Concept / Approach:
Let the cost price be C. Then:

• Selling price at 30% loss = 0.7C.
• Selling price at 40% profit = 1.4C.
• The difference between these two selling prices is given as Rs 140.

So we form the equation 1.4C - 0.7C = 140 and solve for C. This directly gives us the cost price.

Step-by-Step Solution:
Let the cost price be C. Selling price at 30% loss = C - 0.3C = 0.7C. Selling price at 40% profit = C + 0.4C = 1.4C. According to the question, the difference between these two selling prices is Rs 140. Therefore, 1.4C - 0.7C = 140. This simplifies to 0.7C = 140. So C = 140 / 0.7 = 200. Thus, the cost price of the book is Rs 200.

Verification / Alternative check:
Use the cost price C = 200 to verify:

• Selling price at 30% loss = 0.7 * 200 = 140.
• Selling price at 40% profit = 1.4 * 200 = 280.
• Difference between these selling prices = 280 - 140 = 140 rupees, which matches the statement in the question.

Thus the calculated cost price is correct.

Why Other Options Are Wrong:
If C = 280, then 30% loss gives 196 and 40% profit gives 392, difference 196, not 140. With 260, the difference between 0.7 * 260 and 1.4 * 260 is 182. With 300, the difference is 210. With 240, the difference is 168. Therefore, none of these satisfy the condition that the difference between the two selling prices is 140.

Common Pitfalls:
Students sometimes incorrectly set 30% and 40% on the same selling price or forget that the difference of 140 applies to the selling prices, not the percentages themselves. Another frequent mistake is to add percentages directly or use the wrong base for percentage calculations. Always define cost price as a variable and systematically convert loss and profit percentages into algebraic expressions for the selling prices.

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