Comparing Discount Schemes for Maximum Percent Offer

The question asks us to compare three different discount schemes offered by a shopkeeper and identify the scheme that provides the highest discount percentage. Let's analyze each scheme step-by-step.

Scheme I: Successive Discounts Analysis

This scheme involves two successive discounts: 15% followed by 20%.

We can calculate the final discount percentage using the formula for successive discounts:

Discount Percentage = $ D\% = x + y - \frac{xy}{100} $

Where x and y are the two successive discount percentages.

In this case, $ x = 15\% $ and $ y = 20\% $. Plugging these values into the formula:

$ D\% = 15\% + 20\% - \frac{15 \times 20}{100} \% $

$ D\% = 35\% - \frac{300}{100} \% $

$ D\% = 35\% - 3\% $

$ D\% = 32\% $

So, the total discount for Scheme I is 32%.

Scheme II: Buy 4 Get 2 Free Discount

This is an "effective discount" or "buy X get Y free" type of scheme.

In this scheme, you pay for 4 items and receive a total of $ 4 + 2 = 6 $ items.

We can calculate the discount percentage based on the number of items received versus the number paid for.

• Number of items paid for = 4
• Number of free items = 2
• Total number of items received = 4 + 2 = 6

The discount is effectively on the 2 free items compared to the total items received.

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

$ \text{Discount Percentage} = \frac{2}{6} \times 100\% $

$ \text{Discount Percentage} = \frac{1}{3} \times 100\% $

$ \text{Discount Percentage} \approx 33.33\% $

So, the total discount for Scheme II is approximately 33.33%.

Scheme III: Buy 6 Get 4 Free Discount

Similar to Scheme II, this is another "buy X get Y free" offer.

Here, you pay for 6 items and receive a total of $ 6 + 4 = 10 $ items.

Let's calculate the discount percentage:

• Number of items paid for = 6
• Number of free items = 4
• Total number of items received = 6 + 4 = 10

The discount is on the 4 free items relative to the total items obtained.

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

$ \text{Discount Percentage} = \frac{4}{10} \times 100\% $

$ \text{Discount Percentage} = \frac{2}{5} \times 100\% $

$ \text{Discount Percentage} = 40\% $

So, the total discount for Scheme III is 40%.

Comparison of Discount Percentages

Now, let's compare the discount percentages calculated for each scheme:

Comparing the percentages: Scheme I offers 32%, Scheme II offers approximately 33.33%, and Scheme III offers 40%.

Conclusion: Maximum Discount Percent Scheme Identified

Based on the calculations, Scheme III provides the highest discount percentage (40%).