A shopkeeper marks an item at Rs. 1200 but sells it for Rs. 960.\nUsing these values of marked price and selling price, what percentage discount is he offering on the marked price?

Introduction / Context:
This question again tests your understanding of how to convert a reduction in price into a discount percentage. Such problems are extremely common in shop and market based word problems, where a customer is given a reduction on the marked price. Being able to quickly compute the discount percent from marked and selling prices is an essential exam skill.

Given Data / Assumptions:

• Marked price (MP) of the item = Rs. 1200.
• Selling price (SP) of the item = Rs. 960.
• Discount amount = MP - SP.
• Discount percentage is taken with respect to the marked price.
• All rupee values are exact and there are no additional taxes or charges mentioned.

Concept / Approach:
To find the discount percentage, we use the formula:
Discount% = (Discount / Marked Price) * 100.
So, first calculate the discount as the difference between marked and selling prices. Then divide this discount by the marked price to get the fraction of the original price that has been reduced. Finally, multiply by 100 to express this fraction as a percentage. This direct approach avoids confusion and works for any marked and selling prices.

Step-by-Step Solution:
Step 1: Find the discount amount: Discount = MP - SP = 1200 - 960 = Rs. 240. Step 2: Use the formula: Discount% = (Discount / MP) * 100. Step 3: Substitute the numbers: Discount% = (240 / 1200) * 100. Step 4: Simplify the fraction: 240 / 1200 = 24 / 120 = 1 / 5. Step 5: Compute (1 / 5) * 100 = 20. Step 6: Hence, the discount offered is 20 percent.

Verification / Alternative check:
If the discount is 20 percent, then the customer pays 80 percent of the marked price. Calculate 80 percent of Rs. 1200: (80 / 100) * 1200 = 0.8 * 1200 = Rs. 960. This value matches the given selling price, so our computed discount percentage is fully consistent with the problem data.

Why Other Options Are Wrong:
25 percent: 25 percent of 1200 is 300, so the selling price would be 900, not 960.
12 percent: 12 percent of 1200 is 144, giving a selling price of 1056, which does not match 960.
28 percent: 28 percent of 1200 is 336, which would reduce the price to 864, not 960.
18 percent: 18 percent of 1200 is 216, giving a selling price of 984, not 960.

Common Pitfalls:
A frequent mistake is to divide the discount by the selling price instead of by the marked price, which gives a different and incorrect percentage. Another error occurs when students subtract the selling price from the discount or mix up the numbers. Writing the formula clearly and substituting values carefully helps avoid such confusion.

Final Answer:
The shopkeeper is offering a 20 percent discount on the marked price.