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.
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.
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
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.
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
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.
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.