Question

I want to buy a single bed from a furniture dealer selling it for Rs. 13,080. The dealer tells me that I have to pay sales
tax on the bed at the rate of 9%. Approximately, how much discount should I demand on the bed to be able to make
the purchase for a total amount of Rs. 13,080?​

Answer 1

Given:

I want to buy a single bed from a furniture dealer selling it for Rs. 13,080. The dealer tells me that I have to pay sales  tax on the bed at the rate of 9%.

To find:

Approximately, how much discount should I demand on the bed to be able to make  the purchase for a total amount of Rs.13,080?​

Solution:

Let's assume "x %" represents the rate of discount that I should demand from the dealer.

The marked price of the single bed = Rs. 13080

We know,

$\boxed{\bold{Sales\:Price = Marked \: price - (\frac{Discount}{100}\times Marked \:price ) }}$

∴ The sales price after giving a discount will be,

= $13080 - (\frac{x}{100} \times 13080)$

= $13080 - 130.8x$

Since it is given that I want to make the purchase for a total amount of Rs. 13080 including the sales tax at the rate of 9%, so we can form the equation as:

$13080 = [13080 - 130.8x] + \frac{9}{100} [13080 - 130.8x]$ $\implies 13080 = [13080 - 130.8x] + 0.09 [13080 - 130.8x]$

$\implies 13080 = [13080 - 130.8x] + [1177.20 - 11.772x]$

$\implies 0 = - 130.8x + 1177.20 - 11.772x$

$\implies 130.8x + 11.772x = 1177.20$

$\implies 142.572x = 1177.20$

$\implies x = \frac{1177.20}{142.572}$

$\implies \bold{x = 8.256\%}$ ≈ $\bold{8.26 \%}$

Thus, I should demand a discount of 8.26% on the bed to be able to purchase a single bed for a total amount of Rs. 13,080.

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