Comparing Successive Discount Offers for the Best Deal

When a company offers multiple discounts one after another on the same item, these are called successive discounts. To find out which combination of successive discounts is the best offer for a customer, we need to calculate the single equivalent discount for each offer.

The three offers provided are:

• Offer I: 25% and 15% successive discounts
• Offer II: 30% and 10% successive discounts
• Offer III: 35% and 5% successive discounts

Calculating the Effective Single Discount

Let the original price of an item be \(P\). If two successive discounts of \(d_1\%\) and \(d_2\%\) are applied, the final price will be \(P \times (1 - \frac{d_1}{100}) \times (1 - \frac{d_2}{100})\). The total percentage discount is \(100 - \left(\frac{\text{Final Price}}{P} \times 100\right)\).

Alternatively, the effective single discount (\(D_{eff}\%)\) equivalent to two successive discounts \(d_1\%\) and \(d_2\%\) can be calculated using the formula:

\(D_{eff} = d_1 + d_2 - \frac{d_1 \times d_2}{100}\)

Let's use this formula to calculate the effective discount for each offer.

Offer I: 25% and 15%

Here, \(d_1 = 25\%\) and \(d_2 = 15\%\).

Effective Discount \( = 25 + 15 - \frac{25 \times 15}{100}\)

\( = 40 - \frac{375}{100}\)

\( = 40 - 3.75\)

\( = 36.25\%\)

The effective discount for Offer I is 36.25%.

Offer II: 30% and 10%

Here, \(d_1 = 30\%\) and \(d_2 = 10\%\).

Effective Discount \( = 30 + 10 - \frac{30 \times 10}{100}\)

\( = 40 - \frac{300}{100}\)

\( = 40 - 3\)

\( = 37\%\)

The effective discount for Offer II is 37%.

Offer III: 35% and 5%

Here, \(d_1 = 35\%\) and \(d_2 = 5\%\).

Effective Discount \( = 35 + 5 - \frac{35 \times 5}{100}\)

\( = 40 - \frac{175}{100}\)

\( = 40 - 1.75\)

\( = 38.25\%\)

The effective discount for Offer III is 38.25%.

Comparing the Effective Discounts

Let's compare the calculated effective discounts for each offer:

• Offer I: 36.25%
• Offer II: 37%
• Offer III: 38.25%

For a customer, the best offer is the one that provides the highest effective discount, as this means the customer pays the least amount for the item. Comparing the percentages, 38.25% is the highest value among 36.25%, 37%, and 38.25%.

Therefore, Offer III provides the maximum discount to the customer.

Conclusion

Based on the calculations, Offer III (35% and 5% successive discounts) results in the highest effective discount of 38.25%. This makes it the best offer for the customer.

Revision Table: Successive Discounts Comparison

This table summarizes the key information about comparing successive discounts.

Additional Information: Understanding Discounts

Discounts are reductions in the original price of a product or service. They are often used to attract customers, clear old stock, or as part of promotional strategies. There are different types of discounts:

• Single Discount: A straightforward percentage reduction from the original price (e.g., 20% off).
• Successive/Compound Discounts: Two or more discounts applied one after the other. It's important to remember that each discount is applied to the reduced price, not the original price. For example, a 10% discount followed by a 20% discount does not equal a 30% discount.
• Cash Discount: A reduction in price given for prompt payment.
• Trade Discount: A reduction given by a manufacturer or wholesaler to a retailer on the list price.

Understanding how to calculate effective discounts is crucial for both consumers making purchasing decisions and businesses setting pricing strategies.