A shopkeeper offers the following two discount schemes.

(A) Buy 3 get 4 free
(B) Buy 5 get 6 free

Which scheme has the maximum discount percentage?

The correct answer is Option A: Scheme A ("Buy 3 get 4 free") gives the maximum discount percentage.

To compare the two discount schemes fairly, we need to calculate the discount percentage for each. The key formula is:

\text{Discount \%}=\frac{\text{Number of Free Items}}{\text{Total Items Received}}\times 100

This works because the customer pays for only the purchased items, and the "free" items represent the savings. The total items received (paid + free) is the base against which the discount is measured.

Scheme A: Buy 3, Get 4 Free

- Items paid for = 3
- Items received free = 4
- Total items received = 3 + 4 = 7

\text{Discount \% (A)}=\frac{4}{7}\times 100\approx 57.14\%

Scheme B: Buy 5, Get 6 Free

- Items paid for = 5
- Items received free = 6
- Total items received = 5 + 6 = 11

\text{Discount \% (B)}=\frac{6}{11}\times 100\approx 54.54\%

Comparison:

57.14\%>54.54\%

⇒ Scheme A offers a higher discount (≈ 57.14%) compared to Scheme B (≈ 54.54%).

Intuition: Although Scheme B gives more free items (6 vs 4), it also requires you to buy more (5 vs 3). The ratio of free items to total items is what matters, and Scheme A has a better ratio (\frac{4}{7} > \frac{6}{11}), making it the better deal.