Hiten marks a pen at Rs 9800. After allowing a discount of 20% on this marked price, he still makes a profit of 12%. What is the cost price of the pen in rupees?

Introduction / Context:

This question combines concepts of marked price, discount, and profit. Hiten marks the pen above cost price, gives a discount, and still earns a profit. You are required to find the original cost price. This is a typical profit and loss problem that requires careful percentage handling.

Given Data / Assumptions:

• Marked price M = Rs 9800.
• Discount allowed = 20% on marked price.
• After discount, Hiten earns a profit of 12% on cost price.
• We must determine the cost price C.

Concept / Approach:

First, we use the discount percentage to compute the selling price as a fraction of the marked price. Then we use the profit percentage to express the selling price in terms of cost price. Since both expressions refer to the same selling price, we equate them and solve for cost price. This approach ties together discount and profit percentages clearly.

Step-by-Step Solution:

Verification / Alternative check:

Verify the result by forward calculation. If cost price is Rs 7000, a 12% profit means selling price should be 1.12 * 7000 = Rs 7840. With a 20% discount on a marked price of Rs 9800, selling price is 80% of 9800, which is also Rs 7840. Both conditions agree, confirming that the cost price is indeed Rs 7000.

Why Other Options Are Wrong:

• 7600 and 7200: If either were taken as cost price, the 12% profit would give a selling price that does not match the discounted price from 9800.
• 6500 and 6800: These are too low and lead to larger profit percentages than 12% when combined with the given discounted selling price.

Common Pitfalls:

Students sometimes apply the discount to the cost price instead of the marked price, which changes the whole structure of the problem. Another frequent error is adding or subtracting percentage values directly without converting them to their proper roles (discount on marked price, profit on cost price). Clearly label each quantity and write equations for selling price in two ways to avoid confusion.

Final Answer:

The cost price of the pen is Rs 7000.