To solve this, we'll calculate the net cost of a bill of goods amounting to 100,000 under two different discount schemes:

1. A single discount of 45%.
2. Two successive discounts of 33% and 12%.

Case 1: Single Discount of 45%

The formula to calculate the net cost after a single discount is:

$\text{Net Cost} = \text{Original Price} \times (1 - \text{Discount Rate})$

For a 45% discount: $\text{Net Cost} = 100,000 \times (1 - 0.45) = 100,000 \times 0.55 = 55,000$

Case 2: Successive Discounts of 33% and 12%

When dealing with successive discounts, we first apply the 33% discount, then the 12% discount on the new amount. The formula is:

$\text{Net Cost} = \text{Original Price} \times (1 - \text{First Discount}) \times (1 - \text{Second Discount})$

For 33% and 12% discounts: $\text{Net Cost} = 100,000 \times (1 - 0.33) \times (1 - 0.12)$ $\text{Net Cost} = 100,000 \times 0.67 \times 0.88 = 100,000 \times 0.5896 = 58,960$

Difference in Net Costs:

Now, subtract the two net costs to find the difference: $\text{Difference} = 58,960 - 55,000 = 3,960$

Thus, the difference in the net cost is 3,960.

Would you like more details on any of the steps?

Related Questions:

1. What happens if the second discount is changed to 15%?
2. How does the order of successive discounts affect the final price?
3. Can we apply more than two successive discounts, and how does that change the result?
4. What if the bill amount was changed to 200,000 with the same discount rates?
5. How would the calculation differ if the discount was compounded monthly instead of applied directly?

Tip:

When working with successive discounts, always multiply the remaining percentage amounts instead of adding discounts together.