Question

The price of an item is Rs.5400 with 5% VAT.Find the price without VAT and also find the selling price if 20% discount is given on the price with VAT.


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Answer 1

Answer:

Let the price without VAT be 'Rs. x'.

⇒ Price without VAT = Price with VAT - VAT% of x

⇒ x = Rs. 5400 - 5% of x

$\implies x = 5400 - \dfrac{5}{100} \times (x)\\\\\\\implies x + \dfrac{5x}{100} = 5400\\\\\\\implies \dfrac{100x+5x}{100} = 5400\\\\\\\implies \dfrac{105x}{100} = 5400\\\\\\\implies x = \dfrac{5400\times 100}{105}\\\\\\\implies \boxed{ \bf{x \approx 5142.85}}$

Hence the cost of the item without VAT (Value Added Tax) is Rs. 5142.85 (approx.).

Second part of the question requires us to calculate the selling price after applying a discount of 20% on the Price (inclusive of VAT).

⇒ Selling Price = Price (inclusive of VAT) - Discount   ...(i)

⇒ Discount = Discount% of Price (inclusive of VAT)

Calculating the Discount, we get:

$\implies Discount = \dfrac{20}{100} \times (5400)\\\\\\\implies Discount = \dfrac{5400}{5}\\\\\\\implies \boxed{Discount = Rs.\:1080}$

Substituting the value of Discount in (i), we get:

⇒ Selling Price = Rs. 5400 - Rs. 1080

⇒ Selling Price = Rs. 4320

Hence the selling price of the item after a discount of 20% is Rs. 4320.

Answer 2

Answer:

Price after 8% vat=5400

If the initial price=x

vat=8%

Final price=x+ 8x/100 = (108/100)

Given:- 108x/100 = 5400

x = 5400 × 100/108 = 5000

therefore, the price of hair dryer before VAT was added = ₹5000.