A shopkeeper increases the marked price of an object by 40% above its cost price and then sells it at a discount of 25% on the marked price. If the selling price is Rs 2100, what was the original cost price of the object for the shopkeeper?

Introduction / Context:
This question combines markup and discount concepts. The shopkeeper first marks the price higher than the cost price and then allows a discount to the customer. The final selling price and these percentages are given, and we are required to work backward to determine the original cost price. This is a typical profit and loss problem used to test percentage handling and equation formation.

Given Data / Assumptions:

• Let the cost price be C rupees.
• Marked price is 40% above cost price, so marked price = C + 0.4C.
• Discount offered on marked price = 25%.
• Final selling price after discount = Rs 2100.
• We need to find C, the original cost price.

Concept / Approach:
We use simple percentage relations:

• Marked price = C * (1 + 40/100) = 1.4C.
• Selling price = marked price * (1 - 25/100) = 0.75 * marked price.
• So, selling price SP = 0.75 * 1.4C.
• We equate this SP to 2100 and solve for C.

Step-by-Step Solution:
Let cost price be C. Marked price = C + 40% of C = 1.4C. Discount on marked price = 25%, so selling price = 75% of marked price. Therefore SP = 0.75 * 1.4C. SP = 1.05C. Given SP = 2100, so 1.05C = 2100. C = 2100 / 1.05. C = 2000. Thus the original cost price is Rs 2000.

Verification / Alternative check:
Check using the found cost price:

• Cost price = 2000.
• Marked price = 1.4 * 2000 = 2800.
• Discount = 25% of 2800 = 700.
• Selling price = 2800 - 700 = 2100.

This matches the given selling price exactly. We can also compute the profit: profit = 2100 - 2000 = 100, profit percent = (100 / 2000) * 100 = 5%. Everything is consistent.

Why Other Options Are Wrong:
If cost price were 3000, marked price and discounted value would not result in 2100. Values like 1500, 1750, and 1800 also fail to produce a final selling price of 2100 when the same 40% markup and 25% discount are applied. Only 2000 satisfies the percentage relations correctly.

Common Pitfalls:
One common mistake is to add and subtract percentages directly without understanding that they are applied to different bases. Another is treating selling price as cost price while working backward. Always go stepwise from cost price to marked price to selling price and then reverse the process correctly when solving for cost price from a known selling price.

Final Answer:
The original cost price of the object was Rs 2000.