Understanding the Equivalent Single Discount of Two Successive Discounts

When dealing with discounts in sales and finance, it's often necessary to calculate the equivalent single discount of two successive discounts. This can help in simplifying the calculations and providing a clearer understanding of the overall reduction in price. This article will guide you through the process and provide examples to illustrate the concept.

What is the Equivalent of a Single Discount of Two Successive Discounts of 20% and 20%?

Let's say you have an item priced at z rupees. If you apply two successive discounts of 20% and 20%, the final price will be calculated as follows:

Step-by-Step Calculation

Step 1: Subtract the first discount (20%) from the original price.
Fewer steps to achieve the same result: Payable amount after 20% discount z * 0.80

Step 2: Apply the second 20% discount to the resulting price from Step 1.
Fewer steps to achieve the same result: Payable amount z * 0.80 * 0.70 z * 0.56

Step 3: Express the final price as a fraction of the original price.
Fewer steps to achieve the same result: z * 0.56 (1-0.44)z 1 - 44/100 * z

Step 4: Calculate the equivalent single discount.
Fewer steps to achieve the same result: Required discount 44%

Alternative Method: Testing with 100 as Starting Point

An effective way to demonstrate this is by using a test with 100 as the starting point:

Step-by-Step Procedure

Step 1: Subtract 20% discount from 100.
Fewer steps to achieve the same result: 100 * 0.80 80

Step 2: Apply a further 20% discount to the resulting price.
Fewer steps to achieve the same result: 80 * 0.70 56

Step 3: Calculate the overall single discount.
Fewer steps to achieve the same result: 100 - 56 44%

Step 4: Use the given formula to verify the same.
Fewer steps to achieve the same result: 100 - 100 * 0.80 * 0.70 44%

Further Examples and Verification

Let y be the marked price (MP) of an item in rupees. If the first discount is 20%, the discounted price is:

Step 1: Calculate the first discount.
Fewer steps to achieve the same result: Discounted price y * 0.80

Step 2: Apply the second discount of 20% to the discounted price.
Fewer steps to achieve the same result: Final discounted price (y * 0.80) * 0.70 0.56y

Step 3: Determine the total discount in rupees.
Fewer steps to achieve the same result: Total discount y - 0.56y 0.46y

Step 4: Calculate the equivalent single discount.
Fewer steps to achieve the same result: Equivalent discount (0.46y / y) * 100 46%

Another verification using the previous steps shows:

Marked price (MP) y rupees

Total discount 46y/125 rupees

Equivalent discount (100 / y) * (46y / 125) 36.8%

Conclusion

To summarize, the equivalent single discount of two successive 20% discounts applied to an item is 44%. This concept is useful in various economic and financial scenarios where understanding the total impact of multiple discounts is necessary.

By mastering this calculation, you can simplify your financial analysis and make more informed decisions. If you have any questions or need further assistance, feel free to reach out to us.