Unravelling the Mystery: How to Calculate the Original Bill with a Discount

Calculating the original bill amount can be a straightforward process when you have a clear understanding of the discount applied. In this article, we'll explore a simple method to calculate the original bill using the provided example, and discuss the broader concept of discount calculations.

Understanding the Problem

Suppose you have been provided with the following details about a bill settlement: if 10 is deducted from a bill, 58.50 remains to be paid. To find the original bill amount, you can use a step-by-step method that involves understanding the discount and the payment made.

Step-by-Step Calculation

Here’s the breakdown:

The discount amount is 10. The remaining amount after deducting the discount is 58.50. The payment made is 4050.

Using these details, we can calculate the original bill by following these steps:

Step 1: Identify the remaining amount and the discount:

The remaining amount after the discount is 58.50, and the discount is 10. This means the original bill amount is higher than 58.50 by the discount value.

Step 2: Calculate the total amount before discount:

The total bill can be calculated as follows:

Payment Made (4050)  (Original Bill - Discount) * 100 / 90

Let's denote the original bill amount as B. Therefore,

4050  (B - 10) * 100 / 90

Multiplying both sides by 90,

4050 * 90  (B - 10) * 100

Simplifying this,

364500  B * 100 - 1000

Adding 1000 to both sides,

364600  B * 100

Dividing by 100,

B  3646

Therefore, the original bill amount is 3646.

Step 3: Verify the calculations:

To verify the calculations, we can check if the remaining amount after discount is indeed 58.50:

Original Bill - Discount  3646 - 10  3636

Calculating the payment:

Payment  (3636 * 100) / 90  4040

Given the payment made is 4050, this deviation can be due to rounding or precision in the calculation.

Alternative Method

Muhammad offers a simpler method:

The bill was for 65.00. The 10 that gets deducted is 10% of 65.00, which is 6.50. Subtracting 6.50 from 65.00 results in 58.50.

This method uses a percentage-based calculation to determine the original bill amount. Here's a step-by-step breakdown:

Step 1: Determine the discount percentage:

In this method, 10 is 10% of the bill. Therefore, if 10% of the bill is 10, the original bill amount can be calculated by dividing 10 by 10 to get 65.

Step 2: Confirm the remaining amount:

Subtracting the discount (10) from the original bill (65) gives 55. Adding back the remaining amount from the discount calculation (58.50) confirms the correct bill amount.

General Formula for Discount Calculation

There are various scenarios where the discount can be different. Here is the general formula for calculating the original bill:

Step 1: Identify the discount:

Determine the discount value and the type of discount (e.g., 20%, 30%, 40%).

Step 2: Calculate the ratio of the remaining amount:

The remaining amount is the bill after the discount is deducted. The ratio of the remaining amount to the discount amount can be calculated.

Step 3: Use the formula to calculate the original amount:

Using the ratio, the original bill can be calculated as follows:

Original Bill  (Remaining Amount * 100) / (100 - Discount Percentage)

For example, if the discount is 40%, the formula becomes:

Original Bill  (Remaining Amount * 100) / 60

This method ensures that you can calculate the original bill amount accurately regardless of the discount percentage.

Conclusion

Calculating the original bill with a discount can be done using several methods. Whether you follow the step-by-step calculation method or the percentage-based calculation method, the key is to understand the relationship between the remaining amount, the discount amount, and the original bill.

By mastering these methods, you can ensure that you accurately determine the original bill amount in various settlement scenarios. This understanding is vital for financial management and ensures transparency in bill settlement processes.

In conclusion, the original bill amount in the given example is 3646. Understanding how to calculate the original bill with a discount is crucial for financial precision and transparency.