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i) A woman paid Rs. [tex]$1,35,500[tex]$[/tex] for a necklace with a VAT of [tex]$[/tex]13\%$[/tex].

(a) Find the price of the necklace without VAT.

Sagot :

GinnyAnswer
Sure, let's break down the solution step by step:

i) We know the total price paid for the necklace, which includes VAT, is Rs. 1,35,500.

ii) The VAT rate applied is 13%.

iii) To find the original price of the necklace (without VAT), we need to determine what portion of the total price is attributed to the VAT and subtract that from the total price. However, a more efficient way is to use the following relationship:

Total Price with VAT = Price without VAT + VAT Amount

We can also express the VAT amount in terms of the Price without VAT:
VAT Amount = (VAT Rate) (Price without VAT)

From these equations, we can write:
Total Price with VAT = Price without VAT + (VAT Rate) (Price without VAT)

Combining like terms, we get:
Total Price with VAT = Price without VAT * (1 + VAT Rate)

So, to isolate the Price without VAT:
Price without VAT = Total Price with VAT / (1 + VAT Rate)

iv) Plugging in the values:

Total Price with VAT = Rs. 1,35,500
VAT Rate = 13% = 0.13 (expressed as a decimal)

Price without VAT = 1,35,500 / (1 + 0.13)
Price without VAT = 1,35,500 / 1.13
Price without VAT ≈ Rs. 1,19,911.50

Therefore, the price of the necklace without VAT is approximately Rs. 1,19,911.50.
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