In a clothing sale, if 2 T-shirts are offered free on the purchase of 5 T-shirts at the same marked price, what is the effective percentage discount on each T-shirt for the customer?

Introduction / Context:
This percentage based aptitude question tests the idea of effective discount when free items are given as part of a promotional offer. Instead of directly cutting the marked price, the shop offers additional T-shirts free with a fixed number of paid T-shirts. Many students confuse such offers with simple percentage discount, so understanding the relation between number of items received and money actually paid is very important for banking, SSC and other competitive exams.

Given Data / Assumptions:

• A customer buys 5 T-shirts and gets 2 T-shirts free in the same offer.
• All 7 T-shirts have the same marked price per T-shirt.
• The customer pays only for 5 T-shirts and receives 7 T-shirts in total.
• We assume the marked price of each T-shirt to be the same convenient value to compute the effective discount percentage.

Concept / Approach:
The key concept is that effective discount equals reduction in price per unit, expressed as a percentage of the marked price. When free units are bundled, the customer receives more quantity for the same amount of money. We take an assumed marked price, calculate what the customer would pay without any offer, then compare it with the effective cost per T-shirt under the offer. Finally, we compute the percentage discount as (marked price − effective price) / marked price * 100. Choosing a simple assumed marked price, like Rs 100 per T-shirt, keeps the calculation easy without changing the percentage result.

Step-by-Step Solution:
Step 1: Assume the marked price of each T-shirt is Rs 100 (any convenient value works). Step 2: Without offer, to get 7 T-shirts, the customer would pay 7 * 100 = Rs 700. Step 3: Under the offer, the customer pays for only 5 T-shirts: 5 * 100 = Rs 500, but receives 7 T-shirts. Step 4: Effective price per T-shirt under the offer = total amount paid / total T-shirts received = 500 / 7 ≈ Rs 71.43. Step 5: Discount per T-shirt = marked price − effective price = 100 − 71.43 ≈ 28.57. Step 6: Effective discount percentage = (28.57 / 100) * 100% ≈ 28.57% = 28 4/7%.

Verification / Alternative check:
An alternate way is to view the offer as giving 2 free out of 7 T-shirts. Fraction of free T-shirts = 2/7. Therefore effective discount = (2/7) * 100% = 200/7% = 28 4/7%. This matches our earlier calculation based on rupee values, confirming that the assumed price method is valid and that the effective discount does not depend on the actual marked price of each T-shirt.

Why Other Options Are Wrong:

• 40% assumes 2 free out of 5, which ignores that the customer actually receives 7 T-shirts.
• 20% would be correct if only 1 out of 5 were free, which is not the case here.
• 30% is a rough guess close to the correct value but not mathematically accurate.
• 25% would correspond to 1 free out of 4 T-shirts or similar offers, which again does not match this situation.

Common Pitfalls:
Students often divide 2 by 5 instead of 2 by 7 and conclude that the discount is 40%, which is incorrect because they ignore the total number of T-shirts received. Another common error is to treat the offer as a direct reduction in price, without relating it to the per unit cost. Some test takers also forget that percentages should be calculated on the marked price of one item, not on the number of items paid for. Careful identification of the base quantity is essential in discount questions involving free items.

Final Answer:
The effective discount on each T-shirt is 28 4/7%.