Understanding Successive Discounts and Their Impact on Purchaser Benefit

When two shopkeepers sell identical machines at the same marked price, the different discount strategies can significantly affect the final cost for the purchaser. In this analysis, we will compare two sets of successive discounts to determine which series offers the most advantageous purchase price.

Analyzing Discount Series from Shopkeeper 1

Shopkeeper 1 offers a combination of two successive discounts - 30% and 6%. Let's break down the calculation step by step:

Let the marked price (MP) of the machine be P. First Discount: 30% Price after first discount: P × 1 - 0.30 P × 0.70 Second Discount: 6% Final price: P × 0.70 × 1 - 0.06 P × 0.70 × 0.94 Calculation: P × 0.70 × 0.94 P × 0.658

Analyzing Discount Series from Shopkeeper 2

Now let's compare the discount series offered by Shopkeeper 2, which includes 20% and 16% successive discounts:

Let the marked price of the machine be P. First Discount: 20% Price after first discount: P × 1 - 0.20 P × 0.80 Second Discount: 16% Final price: P × 0.80 × 1 - 0.16 P × 0.80 × 0.84 Calculation: P × 0.80 × 0.84 P × 0.672

Final Price Comparison

Through the calculations, we find:

Final price from Shopkeeper 1: P × 0.658 Final price from Shopkeeper 2: P × 0.672

Since 0.658 , the discount series 30% and 6% from Shopkeeper 1 results in a lower final price, making it more advantageous for the purchaser.

Practical Example and General Insights

To further illustrate, let's consider the marked price of both machines A and B to be Rs 100:

Sale price of machine A with successive discounts 30% and 6%: Rs 100 × 0.70 × 0.94 Rs 65.80 Sale price of machine B with successive discounts 20% and 16%: Rs 100 × 0.80 × 0.84 Rs 67.20

Thus, the discounts of 30% and 6% from Shopkeeper 1 offer a lower sale price and are more beneficial to the purchaser.

c) Let's consider another example to delve deeper into the concept of successive discounts. Suppose the total discount is 40% but is distributed unevenly. For instance:

First Discount: 30%, Second Discount: 10%: Sale Price Rs 100 × 0.70 × 0.90 Rs 63 Both discounts of 20%: Sale Price Rs 100 × 0.80 × 0.80 Rs 64

In this case, the unevenly distributed successive discounts, even with the same total discount, yield a higher sale price and are less beneficial to the purchaser.

Therefore, the general insight is that even distribution of the total discount, such as 30% and 6% or 20% and 20%, tends to yield a more advantageous purchase price compared to unevenly distributed discounts.