Shortcut Trick
Scheme (i): Effective discount ⇒ 10 + 20 − (10 × 20)/100 = 28%.
Scheme (ii): Buy 1 Get 1 ⇒ 1/2 × 100 = 50%.
Scheme (iii): Buy 5 Get 3 Free ⇒ 3/8 × 100 = 37.5%.
Scheme (iv): Buy 5 Get 6 (Total) ⇒ 1/6 × 100 = 16.67%.
Comparing all, 16.67% is the minimum discount.
∴ The correct answer is (iv).
Alternate Method
Given: Four discount schemes (i), (ii), (iii), and (iv).
Formula Used: Discount % = (Free items ÷ Total items) × 100
Calculation:
Scheme (i): Two successive discounts of 10% and 20%
⇒ Total Discount % = x + y − (xy)/100
⇒ 10 + 20 − (10 × 20)/100 = 30 − 2 = 28%
Scheme (ii): Buy 1 get 1 free
⇒ Discount % = [Free item / (Paid + Free items)] × 100
⇒ [1 / (1 + 1)] × 100 = 1/2 × 100 = 50%
Scheme (iii): Buy 5 get 3 free
⇒ Discount % = [3 / (5 + 3)] × 100 = 3/8 × 100 = 37.5%
Scheme (iv): Buy 5 get 6
⇒ Here, the customer gets 6 items in total but pays for only 5. Thus, 1 item is free.
⇒ Discount % = (1 / 6) × 100 ≈ 16.67%
∴ Comparing 28%, 50%, 37.5%, and 16.67%, the minimum value is 16.67%.
∴ The correct answer is (iv).
Additional Information
Successive Discounts
When two discounts a% and b% are given successively, the single equivalent discount is (a + b − ab/100)%.
Buy X Get Y Free Concept
In this scheme, the total items received are (X + Y), and the discount percentage is calculated as [Y / (X + Y)] × 100%.
Marked Price and Selling Price
Selling Price (SP) = Marked Price (MP) × (100 − Discount%)/100. Higher discount results in lower SP.