Calculating the Marked Price and Total Amount Paid: A Comprehensive Guide
Understanding the interplay between marked price, discount, and VAT is crucial for effective financial communication and decision-making. This article delves into solving a specific problem: determining the marked price of an article and the total amount paid by a customer who buys the item at a 13% discount and pays Rs 16 VAT, given that they pay Rs 261 as VAT for a total of Rs 261.
Understanding the VAT Payment
Let's begin by understanding the VAT payment. The problem states that the VAT paid is Rs 261, which represents 16% of the selling price (SP).
Step 1: Calculate the Selling Price (SP)
The VAT formula is:
VAT 0.16 × SP
Substituting the given VAT value:
261 0.16 × SP
Solving for SP:
SP 261 / 0.16 1631.25
Find the Cost Price (CP)
The selling price is the marked price (MP) after a 13% discount has been applied. Let the marked price be x.
Step 2: Express the SP in terms of MP
The SP after a 13% discount can be expressed as:
SP MP - 0.13 × MP 0.87 × MP
We know SP is 1631.25. So, we can solve for MP:
0.87 × MP 1631.25
MP 1631.25 / 0.87 ≈ 1875
Calculate the Total Amount Paid
The total amount paid includes the selling price and the VAT.
Step 3: Calculate the Total Amount Paid
Total Amount Paid SP VAT
Total Amount Paid 1631.25 261 1892.25
Summary
Marked Price (MP): Rs 1875
Total Amount Paid: Rs 1892.25
Alternative Methods for Solving the Problem
Understanding the problem from different angles can provide additional insights and methods for solving similar problems.
Method 1: TRADE METHOD
Apply a multiplication factor to find the original price.
Step 4: Use the Hypothetical Price
Assume a hypothetical price of Rs 1000.
Price after 20% discount:
1000 × 0.80 800
Price after adding 13% VAT:
800 × 1.13 904
The multiplication factor is:
1000 / 904
Actual original price:
1000 / 904 × 3616 4000
Method 2: LONG METHOD
Remove the VAT first and then add the discount.
Step 5: Remove 13% VAT from the final price
Divide the final price by 1 VAT percentage:
3616 / (1 0.13) 3616 / 1.13 3200
Step 6: Add back the 20% discount
3200 × (1 0.20) 3200 × 1.20 3840 × 1.05 4000
Method 3: COMBINED METHOD
Directly calculate the marked price using the combined formula:
3616 / (113/100) × (100/80) 4000
Verification:
If MP 4000, the price after 20% discount:
4000 × 80/100 3200
Price on 13% VAT:
3200 × 0.13 416
Final price 3200 416 3616
Conclusion
This comprehensive guide detailed the step-by-step process for calculating the marked price and the total amount paid, offering different methods to ensure a deep understanding of the underlying financial calculations. Effective communication of these concepts allows for better decision-making and transparency in financial transactions.