Question

The marked price of an article is 5000 if the discount rate and vat rate are equal and the price with vat is 4950 find the discount rate

Answer 1

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Answer 2

The Discount rate on the article is 10%

Step-by-step Explanation:

Given:

• Marked Price (MP) of Article = Rs. 5000
• Discount Rate and VAT rate are equal
• Selling Price (SP) with VAT = Rs. 4950

To be found: The Discount rate on the article

Formula used:

• SP = MP – [(Discount%/100)*MP]

• SP with VAT = [(100 + VAT%)/100]*SP

Where:

SP – Selling Price

MP – Marked Price

Discount % - the discount percentage applied to the product

SP with VAT – the final Selling price after reducing VAT%

Solution:

Assuming VAT% to be x

As its given VAT% = Discount %

then Discount% = x

Using formula:

SP = MP – [(Discount%/100)*MP]

SP = 5000 – [(x/100)*5000]

SP = 5000 – 50x

This is our first equation.

Using second formula:

SP with VAT = [(100 + VAT%)/100]*SP

4950 = [(100 + x)/100] * (5000 – 50x)

Replacing the value of SP with the value in the first equation.

4950 = [1 + (x/100)] * (5000 – 50x)

4950 = 5000 - 50x + (5000x/100) – (50x²/100)

4950 = 5000 – 50x + 50x – (x²/2)

4950 – 5000 = -x²/2

-50 = -x²/2

Cancelling the negative from both sides

x²/2 = 50

x² = 100

√x = 10

So, VAT% = x = 10%

As VAT% = Discount % = 10%

Hence the discount% on the article is 10%