The marked price of an article is 20% more than its cost price. If a shopkeeper gives a discount of 5% on the marked price, what is the profit percentage earned on the cost price?

Introduction / Context:
This question combines the concepts of marked price, discount and profit. The article is first marked up over its cost price and then a discount is given on that marked price. Even after giving the discount, the shopkeeper still makes a profit. We must compute the final profit percentage on the cost price after both operations.

Given Data / Assumptions:

• Let the cost price (CP) of the article be C rupees.
• Marked price (MP) is 20% more than CP, i.e., MP = 1.20C.
• Discount given on MP = 5%.
• We must find the profit percentage on C after applying the discount.

Concept / Approach:
First, we calculate the selling price by applying the discount to the marked price. Selling price SP = MP * (1 − discount). Once SP is known in terms of C, the profit is SP − CP and the profit percentage is (SP − CP) / CP * 100. Since both operations are simple percentages, the algebra remains straightforward.

Step-by-Step Solution:
Assume cost price = C rupees. Marked price MP is 20% more than C, so MP = C * 1.20 = 1.20C. Discount on marked price = 5%. Therefore, selling price SP = MP * (1 − 0.05) = 1.20C * 0.95. SP = 1.140C. Profit = SP − CP = 1.140C − C = 0.140C. Profit percentage = (Profit / CP) * 100. Profit percentage = (0.140C / C) * 100 = 14%.

Verification / Alternative check:
Let C = Rs. 100 for an easy check. Then MP = 120% of 100 = Rs. 120. Discount of 5% on MP means discount amount = 5% of 120 = Rs. 6. New selling price SP = 120 − 6 = Rs. 114. Profit = SP − CP = 114 − 100 = Rs. 14. Profit percentage = (14 / 100) * 100 = 14%. This confirms that the calculated percentage is correct.

Why Other Options Are Wrong:
5% and 10%: These underestimate the true profit because they effectively treat the net increase incorrectly after markup and discount.
15% and 25%: These overestimate the profit. 25% would correspond to keeping the full 20% markup without discount plus extra, which is not the case here.

Common Pitfalls:
One common mistake is to add or subtract percentages directly, for example computing 20% − 5% = 15% and concluding that profit is 15%. This ignores the fact that 5% discount is calculated on the marked price, which is itself 20% higher than cost. The correct method is to multiply the successive percentage factors, 1.20 and 0.95, and then compare with 1.00 (the cost price base).

Final Answer:
The shopkeeper earns a profit of 14% on the cost price.