Question

A radio labeling Rs. 1000 is sold at Rs. 990 by levying VAT after allowing certain discount. If the rate of discount so allowed is equal to the rate of VAT so levied on it, find the rate of discount.​

Answer 1

Explanation:

Let's assume that the rate of discount is x%, and the rate of VAT is also x%.

According to the problem, the radio is sold at Rs. 990 after allowing a discount. So, the selling price of the radio after the discount is:

Selling price = Rs. 1000 - x% of Rs. 1000

Selling price = Rs. 1000 - (x/100) * Rs. 1000

Selling price = Rs. 1000(1 - x/100)

Selling price = Rs. 10 * (100 - x)

Now, VAT is levied on this selling price at the rate of x%. So, the final selling price after VAT is:

Final selling price = Selling price + VAT

Final selling price = Rs. [10 * (100 - x)] + x% of [10 * (100 - x)]

Final selling price = Rs. [10 * (100 - x)] + (x/100) * [10 * (100 - x)]

Final selling price = Rs. [10 * (100 - x)][1 + x/100]

Final selling price = Rs. 990

Substituting the value of Rs. 990, we get:

Rs. 990 = [10 * (100 - x)][1 + x/100]

99 = (100 - x)(1 + x/100)

99 = 100 - x + x - x^2/100

x^2/100 = 1

x^2 = 100

x = ±10

Since the discount cannot be negative, the rate of discount is 10%. Therefore, the rate of VAT is also 10%.

So, the radio was sold at Rs. 1000 - 10% of Rs. 1000 = Rs. 900 after allowing a discount of 10%, and VAT of 10% was levied on this selling price, which makes the final selling price Rs. 990.