# Mark-ups and Discounts Involving Sales Tax

We will discuss here how to solve the problems based on mark-ups and discounts involving sales tax.

1. Davis bought a car listed at $536500 at 8% discount and then 10% sales tax charged on the discounted price. Find the amount Davis paid for the car. Solution: Price listed on the car =$ 536500, rate of discount = 8%

Therefore, the amount of discount = $(536500 X 8/100) =$ 42920

Therefore, the selling price of the car = $(536500 - 42920) =$ 493580.

The rate of sales tax = 10%

Therefore, the sale tax on the car = $(493580 X 10/100) =$ 49358

Therefore, the amount paid by Davis = $(493580 + 49358) =$ 542938.

2. Ron buys a car for $38,400 which includes 10% discount and then 6% sales tax on the marked price. Find the marked price of the car. Solution: Let the marked price of the car be P. Then, the discount on marked price = 10% of P = 10/100 P = P/10, and sales tax = 6% of P = 6/100 P = 3P/50 Therefore, the price paid = P – P/10 + 3P/50 = 50P – 5P + 3P/50 = 48P/50 = 24P/25 According to the problem we get, 24P/25 =$38400

P = $38400 × 25/24 =$1600 × 25

= $40000 Therefore, the marked price of the car is$40000.

3. Due to short supply in the market, a shopkeeper raises the price of a cycle by 5% above the marked price and charges a sales tax of 12 % on the marked price. A customer has to pay $4680 for the cycle. Find the marked price of the cycle. Solution: Let the marked price of a cycle be P. Then, the raised price = P + 5% of P = P + 5P/100 = 21P/20 Sales tax = 12% of P = 12/100 P = 3/25 P Therefore, the price payable = 21P/20 + 3P/25 = 105P + 12P/100 = 117P/100 According to the problem we get, 117P/100 =$4680

P = $4680 × 100/117 =$4000

Therefore, the marked price of the cycle is $4000. 4. Jack buys a laptop for$ 34821 which includes 10% rebate on the listed price and then 6% sales tax on the remaining price. Find the listed price of the computer.

Solution:

Let the listed price of the laptop be $x, rebate on the listed price = 10% Therefore, the amount of rebate =$ (x + 10/100) = $x/10 Therefore, cost of the laptop after rebate =$ x - $x/10 =$ 9/10 x

Since sale tax is 6% on the remaining price,

Therefore, the amount of sales tax= $9/10x X 6/100 =$ 27/500 x.

Therefore, the net amount to be paid = $910x +$ 27/500 x

= $(9/10x + 27/500x) According to the problem, we get, 9/10x +27/500x = 34821 Or, 477/500x = 34821 Or, x = 36500. Therefore, the marked price of the laptop =$ 36500.

● Sales Tax and Value Added Tax