Difference Between a Single 40% Discount and Two Successive Discounts of 36% and 4% on a Bill of Rs. 100,000

Calculating the difference between a single 40% discount and two successive discounts of 36% and 4% on a bill of Rs. 100,000 can be a bit complex, but breaking it down step-by-step makes it quite clear. Let's dive into the calculations and see how the final prices differ.

Single Discount of 40%

The formula for calculating the price after a single discount is:

Final Price Original Price times; (1 - Discount Rate)

For a 40% discount:

Final Price 100,000 times; (1 - 0.40) 100,000 times; 0.60 60,000

Successive Discounts of 36% and 4%

When applying successive discounts, we calculate them one after the other. Let's break this down step by step:

Price after 36% discount 100,000 times; (1 - 0.36) 100,000 times; 0.64 64,000

Now, apply the 4% discount to the new price:

Final Price 64,000 times; (1 - 0.04) 64,000 times; 0.96 61,440

Difference Between the Two Final Prices

Now that we have the final prices from both scenarios, we can find the difference:

Difference Price with a single discount - Price with successive discounts

Difference 60,000 - 61,440 -1,440

The negative value indicates that the price with two successive discounts is lower by Rs. 1,440 compared to the single discount.

Conclusion

The difference between a single 40% discount and two successive discounts of 36% and 4% on a bill of Rs. 100,000 is Rs. 1,440 in favor of the two successive discounts. This result can be used in business settings to determine which discount strategy is more cost-effective.

Additional Insights

For a deeper understanding of discount calculations, we can consider the effective discount formula for two successive discounts:

Effective Discount xy - (xy/100) 36 times; 4 - (36 times; 4)/100 144 - 1.44 142.56

Therefore, the effective discount as a percentage of the original price is:

Effective Discount % (142.56/100,000) times; 100 1.4256%

Converting this to a less than 1% value gives us the difference of Rs. 1,440 as calculated earlier.