What is the effective percentage discount when an offer says "Buy 6 and get 1 free" on identical items?

Introduction / Context:
This is a percentage discount question disguised as a promotional offer. The phrase "Buy 6 and get 1 free" means the customer receives 7 items but pays for only 6. To find the effective percentage discount, we compare the price that would have been paid for all 7 items at full price with the reduced price paid under the offer. These kinds of problems are common in profit and loss or percentage sections of aptitude tests.

Given Data / Assumptions:

• All items are identical and have the same marked price.
• Under the offer, the customer pays for 6 items and gets 1 item free, receiving 7 items in total.
• The normal situation without discount would be paying full price for all 7 items.
• We must compute the percentage discount relative to the total full price.

Concept / Approach:
Let the price of one item be P. Without any offer, 7 items would cost 7P. With the offer, the customer receives 7 items but pays only 6P. The discount in rupees is the difference between 7P and 6P, which is P. The percentage discount is the discount amount divided by the original full price (7P) multiplied by 100. The price P cancels out in the ratio, which means the discount percentage is independent of the actual price per item.

Step-by-Step Solution:
Step 1: Let the price of one item be P.Step 2: Without any offer, the cost of 7 items = 7P.Step 3: Under the offer "Buy 6 and get 1 free," the customer pays for 6 items and gets 7 items in total, so the amount paid = 6P.Step 4: Discount in rupees = original full cost - offer cost = 7P - 6P = P.Step 5: Percentage discount = (Discount / original full cost) * 100 = (P / 7P) * 100.Step 6: Simplify (P / 7P) * 100 to (1 / 7) * 100 ≈ 14.285 percent.

Verification / Alternative check:
Take a simple price, say P = Rs. 70. Then 7 items at full price would cost 7 * 70 = Rs. 490. Under the offer, the customer pays 6 * 70 = Rs. 420. The discount is 490 - 420 = Rs. 70. The percentage discount is 70 / 490 * 100 = 1 / 7 * 100 ≈ 14.285 percent. This matches the earlier algebraic calculation. The result does not depend on the particular value chosen for P.

Why Other Options Are Wrong:
The values 85.78 percent and 58.48 percent and 19.25 percent and 25 percent do not correspond to (1/7) * 100. For example, a discount of 25 percent would mean paying only 75 percent of the full price, which here would correspond to paying for 5.25 items instead of 6, which is not the offer. Only 14.285 percent matches the ratio of 1 free item out of 7 received.

Common Pitfalls:
Many students mistakenly divide by 6 instead of 7 or treat the discount as 1/6 of the price rather than 1/7 of the full cost of 7 items. Others confuse the number of items received with the number of items paid for, leading to incorrect ratios. Keeping track of the baseline for percentage calculation, which is the full cost of 7 items, is essential.

Final Answer:
The effective percentage discount in a "Buy 6 and get 1 free" offer is 14.285%, so the correct option is 14.285%.