A shop offers a deal in which 1 shirt is given free on the purchase of 4 shirts of the same price. What is the effective discount percentage on each shirt due to this offer?

Introduction / Context:

This question presents a common promotional scheme: buy a certain number of items and get one free. You need to convert this type of offer into an equivalent percentage discount. Such questions are standard in profit and loss and percentage topics and help in understanding effective discounts in real-world offers.

Given Data / Assumptions:

• The offer is: buy 4 shirts and get 1 shirt free.
• All shirts have the same marked price.
• The buyer ultimately receives 5 shirts but pays only for 4 shirts.
• We need the effective discount percentage per shirt.

Concept / Approach:

Let the marked price of each shirt be P. Under the offer, the customer gets 5 shirts but pays 4P. The effective price per shirt is total amount paid divided by number of shirts received. The effective discount percentage is then computed by comparing this effective price per shirt with the original marked price P.

Step-by-Step Solution:

Verification / Alternative check:

Assume a simple numerical price, say P = Rs 100. Without any offer, 5 shirts would cost Rs 500. With the offer, the customer pays 4 * 100 = Rs 400 and receives 5 shirts. Effective price per shirt = 400 / 5 = Rs 80. The discount per shirt is 100 − 80 = Rs 20, which is 20% of 100. This confirms the 20% effective discount.

Why Other Options Are Wrong:

• 25%: This would imply paying Rs 75 per Rs 100 shirt, which does not match the computed Rs 80 effective price.
• 16% or 24%: These values correspond to different ratios between amount paid and items received; they are not consistent with a 4-for-5 scheme.
• 30%: This would mean a much larger reduction than the actual effect of the offer.

Common Pitfalls:

Students sometimes treat 1 free out of 5 as 20% of the number of shirts and directly state the discount as 20% without checking if it matches the price calculation. While in this case it coincidentally matches, it is safer to compute using the total amount paid and total quantity received. This approach generalises more reliably to similar but slightly different offers.

Final Answer:

The effective discount on each shirt is 20%.