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





10th Grade Math

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